Speaking bluntly, "Delaying your turn" or refusing to participate in the initiative roll, in a combat in which you otherwise intend to participate, is not an option. There is no rule that allows this, and 5e designers are registered because they specifically do not want to allow things that allow mutability to the initiative because it interferes with the duration of the effects (which are usually related to the turn of the person who produced the effect).
I would also like to issue a framework challenge: I do not believe that the specific problem you are trying to solve is unique to having a high initiative score. I think it is also very common with a low initiative score.
Speaking as someone who has had to play a Paladin in scenarios in which my allies frequently bounced between 0 and were aware several times in a row in combat, the specific problem you are describing almost always occurs whenever the BBEG has its turn directly after your own. You heal your ally, who is then quickly beaten by the BBEG, recognizing that his previous quarry has woken up again. In the meantime, your ally has no opportunity to act on their turn (and depending on how fixed the BBEG is in them, they could be risking their last Death Saving Throw!). The trick here is that it is the same problem, regardless of whether you took 25 and the BBEG took 24, or if you took 5 and the BBEG took 4: if your turn is (relatively speaking) after yours, and between you and your vulnerable ally , you will continue to have this problem.
And, in general, automatically obtaining an Initiative of 1 does not guarantee the solution of the problem. The BBEG could shoot a 27, and once again we are on the same stage.
So, the solution is to strategically take advantage of the Ready action.
Sometimes you want to jump on an enemy or wait for a particular circumstance before acting. 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 perceptible circumstance will trigger your reaction. Then, you choose the action you will take in response to that trigger, or you choose to advance at your speed in response to it. Examples include "If the cultist steps on the trapdoor, I will pull the lever that opens it" and "If the elf steps on my side, I walk away."
When the trigger occurs, you can take your reaction right after the trigger ends or ignore it. Remember that you can only take one reaction per round.
When you prepare a spell, you cast it as normal but maintain its energy, which you release with your reaction when the trigger occurs. To be prepared, a spell must have a cast time of 1 action, and maintaining the magic of the spell requires concentration (explained in Chapter 10). If your concentration is broken, the spell dissipates without effect. For example, if you are concentrating on the web spell and the ready magic missile, your web spell ends, and if you take damage before launching the magic missile with your reaction, your concentration could break.
You have until the beginning of your next turn to use a prepared action.
–Ready action, Player Manual, p. 193
The sequence you will want is something like this, done before any of your allies have fallen (but after their health has become quite low, in response to which you have moved alongside them):
* I will prepare the spell To heal wounds, and if an ally falls unconscious, after the enemy stops attacking it, I will use the spell to retrieve it. *
Of course, you can reformulate the trigger differently according to your needs. If the BBEG is relentlessly attacking a single character, even through unconsciousness, it is likely that he should activate the trigger right after unconsciousness rather than "when they stop being attacked."
Regardless, however, what this achieves is that if an Ally falls, they heal immediately, allowing them to take their turn in the usual way, hoping they can disengage and get away from the BBEG.
This, for me, solves the problem you face, where the Allies may suddenly fall due to Critical Impact damage.