So bluntly speaking, "Delaying your turn" or otherwise refusing to participate in the initiative roll, in a combat where you otherwise intend to participate, isn't an option. There's no rule that permits this, and the 5e designers are on record as specifically not wanting to allow stuff that allows mutability to initiative because it messes with the durations of effects (which are usually keyed to the turn of the person who produced the effect).
I would also like to issue a frame challenge: I don't think the specific problem you're trying to fix actually is unique to having a high initiative score. I think it's also very common with a low initiative score.
Speaking as someone who has had to play a Paladin in scenarios where my allies were frequently bouncing between 0 and conscious multiple times in a row in combat, the specific issue you're describing pretty much always occurs whenever the BBEG has their turn directly after your own. You heal your ally—who is then promptly beaten back into the dirt by the BBEG, recognizing that their previous quarry has woken back up. Your ally, meanwhile, gets no chance to act on their turn (and depending on how fixated the BBEG is on them, they might be risking their final Death Saving Throw!). The trick here is that it's the same problem, regardless of whether you rolled 25 and the BBEG rolled 24, or you rolled 5 and the BBEG rolled 4: If their turn is (relatively speaking) after yours, and between you and your vulnerable ally, you're going to continue to have this problem.
And in general, automatically getting an Initiative of 1 is no guarantee of fixing the issue. The BBEG could just roll a 27, and we're once again in the same scenario.
So the solution then is to take strategic advantage of the Ready action.
Sometimes you want to get the jump on a foe or wait for a particular circumstance before you act. To do so, you can take the Ready action on your turn so that you can act later in the round using your reaction.
First, you decide what perceivable circumstance will trigger your reaction. Then, you choose the action you will take in response to that trigger, or you choose to move up to your speed in response to it. Examples include "If the cultist steps on the trapdoor, I'll pull the lever that opens it," and "If the goblin steps next to me, I move away."
When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger. Remember that you can take only one reaction per round.
When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs. To be readied, a spell must have a casting time of 1 action, and holding onto the spell's magic requires concentration (explained in chapter 10). If your concentration is broken, the spell dissipates without taking effect. For example, if you are concentrating on the web spell and ready magic missile, your web spell ends, and if you take damage before you release magic missile with your reaction, your concentration might be broken.
You have until the start of your next turn to use a readied action.
—Ready Action, Player's Handbook, pg. 193
The sequencing you'll want is something like this, done before any of your allies have fallen (but after their health has gotten pretty low, in response to which you've moved adjacent to them):
I'm going to ready the spell Cure Wounds, and if an ally falls unconscious, then after the enemy stops attacking them, I'll use the spell on them to get them back up.
Of course, you can reword the trigger differently depending on your needs. If the BBEG is relentlessly attacking a single character, even through unconsciousness, you'll probably need to set the trigger to right after unconsciousness instead of "when they stop being attacked".
Regardless though, what this accomplishes is that if an Ally goes down, they get healed right away, which allows them to take their turn as normal—hopefully permitting them to Disengage and move away from the BBEG.
This, to me, solves the problem you're facing where Allies can suddenly go down due to spiky Critical Hit damage.