Pre-Plan your random encounters, and go deadly more often
I don't think that rest is your actual problem.
we are still unable to fit more than 2-3 resource using encounters between long rests.
Let's look at a key element to a West Marches campaign: DM's get time to prep because the players are organized enough to tell the next DM "we want to head over toward the The Green Tea Swamp for the next session" or words to that effect.
Yes, it's a sandbox, but the players must decide what they would like to do in advance of the session. Normally, as part of booking the DM's time for the session, the players would also state what they wanted to do in that session. This way the DM can prepare in advance, without needing to prepare the whole world, or improvise large pieces of content. (Linked Q&A)
If you are not already doing that as a group, then you need to start doing that effective immediately. Cut the DM-for-the-day a break; give them the opportunity to plan.
Your stated problem is that the encounters aren't taxing enough on the resource base, and your group's time management (based on game session time available) doesn't match your desire to have the ending of the session and the adventure day coincide.
Problem statement: you have to get "back to base" by the end of the session and you have to put a higher demand on resources.
- A significant part of the solution is to keep the pace of play moving.
- The other part is to make the encounters harder.
Do all of your DM's buy into this, or just one or two of you?
If all of your DM's don't buy into this to the level that you do, your problem isn't very solvable unless your whole table accepts that some nights are "easy nights" and some nights are "hard nights" - which some groups accept readily. We had a group that RL broke up two years ago who liked that: some nights are tough nights and some nights are a walk in the park.
We had a problem very like yours in my brother's shared campaign world where I am the other DM (our third is gone for RL reasons) - we do not strictly have a West Marches campaign; mostly we have/had the 'nova' problem and significant RL scheduling and session length challenges (the latter are outside the scope of this answer).
What I noticed was that while some resources were used, there was ample reserve. During a sojourn through the mountains, I raised the stakes as DM. I roughed out 3 deadly+ encounters per day ahead of time; and three hard-to-deadly. What I never knew was "When does this one happen?" but what I was sure of was that at least three would happen. As it worked out, the party tended to be out of resources when the adventure day was done. They occasionally cake walked an encounter, but the dice are fickle - sometimes, that happens. What follows is how I pre-loaded random encounters, taken mostly from a different answer.
Since you are running a West Marches style, the "fight or flee" decision is an imbedded part of the style you all have chosen; you have it easier than I did. In your case, it is OK to make some of the encounters well beyond deadly such that the party has to flee and may have to use resources in order to successfully flee. How to set this up is Reverse XP budgeting. Plan to do 3 (tougher) encounters with 1 or 2 short rests per session, but have 6 or 9 pre packaged that are suitable for the area.
Using the XP-per-day-per-character table in the DMG and work backwards.
Err on the harder side. The example uses 5 level 4 PCs.
A 4th level PC can handle 1,700 XP-per-character-per-day (in theory) before resource exhaustion. With five 4th level characters, there are 8500 adjusted XP worth of monsters to play with for an adventure day. The following three encounters with a short rest between 1 & 2, and between 2 & 3 meets this budget. And you can sometimes only allow 1 short rest.
This approach reduces your problem of "how many encounters": each encounter is a significant challenge. Deadly is estimated as 2500 XP for 5 level 4 characters on the XP Thresholds by Character Level table. (The below examples add up to 8400 XP all told; close enough). Again, you can make them harder if you'd like; it's West Marches - they may need to flee or talk their way out of combat rather than fight. That second level suggestion spell is a resource well expended if it convinces the Stone Giant not to squish the Paladin like a bug. All encounters use the NPC names in MM and Volo's Guide.
- Encounter 1: An Acolyte (re-skinned as a low level shaman) and 3 Berserkers. ((3 x 450 + 50) X 2) = 2800 adjXP
- Encounter 1a: two Hill Giants (2700 adjXP)
- Encounter 2: A Druid, 3 Scouts, and a Veteran (possibly elves who are guarding a sacred grove; and xenophobic regarding outsiders). ((450 + 300 + 700) X 2) = 2900 adjXP.
- Encounter 2a: An Earth elemental and four mud mephits.
- Encounter 3: A wight leading a zombie ogre and four zombies emerges at sunset from the forest / swamp / cave / ruin ... (700 + 450 +200) x 2 = 2700 adjXP.
Encounter 3a: a young black dragon. (2,900 XP)
Caveat: some of these have a lot of NPCs/Monsters. "Focus fire on one enemy" becomes a less effective tactic, and the DM has a bit more work to do in each encounter. Dropping in a CR 7 monster (~ 2900 XP for one encounter) presents a different problem, but is at least easier for the DM to run. As this is West Marches, the chance that a PC may die is IIRC generally accepted. But that's only the first part of the solution. Combat needs to feel dangerous and pressure packed.
Make combat fast and furious
You need to run the combats in a "fast and furious" mode (for two reasons that I'll get to). But please note, this fast and furious mind set is not applied to non-combat encounters. Let those go at an organic pace.
Reason 1: time compression.
In Fast and Furious mode, the players need to feel pressure to make a decision. The player is to do all of their thinking before their turn comes up. They need to pay attention to what is happening in combat; pay attention to what the other players are doing and saying. If someone isn't ready to tell you what they are doing when it's turn in the initiative order, they get to take the Dodge action and you go to the next player's turn. I've done that a few times with slow players: the message got across. I generally allow two questions from the player to help them resolve what's going on - "Is that elephant in range? "Which of those two ogres looks more badly wounded?" This overall approach enhances the feel of combat, and provides a sense of urgency.
Note that if your whole table will not buy into the fast and furious mode of combat, that preference adds to your core problem of time management of a gaming session.
Reason 2: mistakes usually cost resources
Decision making will, over time, improve and combats will take less time, but poor decisions will be made sometimes and will usually create a larger resource demand - which is something that you say that you want.
A potential problem with this approach and with your question
I am not sure that you speak for all of the DMs at your table. (It's great if you do, but I have no way to confirm that).
All of the DMs have to agree to (1) pre-rough in some encounters ahead of their turn to DM and (2) to implement Fast and Furiuos combat. Fast and furious can lead to mistakes in combat, which can (1) lead to overuse of resources or (2) a need to flee - and those outcomes both lead to neat stories (you did what?) and they support your end objectives as stated in the question: at sessions end the party gets back to base and really needs that long rest.
Whether or not your group of DMs are all willing to do this can only be determined by a detailed discussion among you all about:
(1) is this really a problem, or are you the only one seeing it?
(2) does each DM have some time to rough in some deadly encounters that fit the expected regions that the party will be in before their DM session?
That answer can only come from within your group.
A note on Resources to help you (the DMs) do all this: there are a variety of encounter builder tools available on line, but each one has its own nuances. Pick the one that works best for you. It will save time, and will enhance your ability to put 6, 9, or 12 hard-to-deadly-to-worse encounters into a pile before your next DM session - and you only need to run three of them.