Who Has The Problem Here?
This is pushback, but only mild pushback. It's worth considering whether you and your group really have a problem here. It doesn't sound like your players have a problem-- they readily engage with some aspects of the game more than others, but you're not painting a picture of unhappy players, per se.
However, I don't want to discount your own happiness and satisfaction. You're not the player of a PC, but as the GM you are a player and ought to be deriving satisfaction and pleasure from the game. So if this style of play makes the game not fun for you, then that settles the issue. I raise it mainly as food for thought-- you may be assuming that this style of play is just wrong and must be fixed... but if no one is unhappy, then why fix it?
Having raised that possibility, I'll continue on the assumption that, yes, someone is really unhappy about this, and it does need to be fixed.
Short Term Gambits
Even the best players get trapped in a cycle like this occasionally, and most GMs have a personalized set of tricks to remind the players to stop talking and start playing. Mine are pretty in-your-face:
"Okay, guys, you've been in this room with a door for fifteen minutes and nothing has happened. What are you doing, now?"
GMs of my acquaintance remind the players of their agency with a spiel that runs something like: "Okay, you're at a crossroads with a scarecrow-- you can take the left branch, the right branch, dance a musical number with the scarecrow or yell 'The King is a fink!'" It always starts from something grounded into the scene proceeds through the weird, and ends with yelling the King is a Fink. Once they break out King Fink, we know we're being told to move it along, already.
You can also sprinkle your scenes liberally with time pressure, and reference that as a way to get moving again. But this starts to get old really fast if every single room has a count down to destruction.
The point is, don't be afraid to nudge your players. Or shove your players. Or sit them down and explain totally out of character that you need their actions and input to work with. Don't be afraid to teach through editorializing, at least at first.
But those are stop gap or occasional remedies. In the longer run, if you want constant player actions to drive your game, you need something structural.
And by structural, I mean three specific things:
Mandate that your players design characters that care about something. Ideally, the things they care about will intersect. One might care about the village they grew up in, another might care about their sibling in that village, a third might care about the temple in that village they were educated at... whatever. Do not be afraid to make this a requirement of the game. It's difficult, but not impossible, to retroactively add this sort of thing after the fact, but it's best if done early. (more on this later.)
Design a certain amount of dynamism into your game world. If the PCs do nothing, forces and factions act without them, and the world changes. Then...
Threaten everything the PCs know, love, or care about. Threaten to burn it all right to the ground if the players don't act. It's not personal, it's just the natural trajectory of the game world. The orcs aren't attacking the village because the PC's sister lives there-- but she does live there, and will die without PC action. The mind flayers don't give a flying fig about the sacred temple in the dwarven tunnels-- but this other PC does.
Now you can editorialize to your players with a little more dramatic force: "Remember guys, you only have four days to lead a relief force to the village or everyone dies. So, what are you doing?"
This is all, in my opinion, best set up early in the game. Before the game begins, during character creation, in fact. But there are ways to finesse it after the fact. It just takes time.
Your solution about giving the PCs a fixed point to manage, interact with, and defend is one good way. But I would urge you, as GM, to use an opportunity like that to get the characters to care about individual pieces of that setting as they defend it. (I think of this as the Deep Space 9 set-up. Ben Sisko didn't want to be there, initially, but eventually found a purpose in the setting and the other characters.)
Another good way is to set the characters up as part of an organization which can just given them orders in the short term, to provide impetus for some initial short term adventures. But along the way, again, you should be doing everything in your power to make your characters care about other characters in that organization or setting. Then you can transition from just giving them orders to threatening the organization and giving the players responsibility for it.
These are not exhaustive. These are only examples. But they all exploit the same basic pattern: 1) Make the players care, 2) Establish forces in play, and 3) Use those forces to threaten what the characters love.
Threaten a character, and they can run away. Threaten what they love, and you force them to stay and fight.