There was a jenga-less way to play Star Crossed a few years ago that just required a D20 roll. You write out each number, 1 through 20, on a sheet of paper, and when asked to pull a block, you roll the d20 instead. If you hit the same number 4 or 5 times (I think it was 5?), the tower falls.
I'm not sure how that would work with holding onto the blocks for later, though... Just thinking off the top of my head, to modify this, roll a d20 for every pull, and another d20 for every placement, then when the same number comes up 10 times, the tower would fall. Which would work like this:
Player A got Player B to complete a 3 Pull goal.
Player A rolls 1d20 to start the attack and records the result on the sheet and marks that they now have one more block in their hand.
Player B rolls 2d20 three times to defend and records the result of each die.
The next time Player A wishes to have their reserve block added to the tower by another player, that player rolls 1d20 and records the number on the sheet, and Player A records that they no longer have that reserve block.
This should give you a similar tension once a number approaches 8 rolls in a round. Even more tension with each roll if a number is at 9.
Let me know if you end up trying this out. I'd be very curious if it works well.
Thanks for reaching out!