Your current PR strategy is designed for you to max out your score for your current knowledge. To get better you have to learn more tactics, that way you can solve harder puzzles.
That means don't quit once you fail a puzzle because it's better to get higher rated puzzles and fail those so you can study them. Also don't try to use meta-games. For example you say "this is a low rating so it's not a non-forcing move, I'll just guess a random check and hope it works" -- this is obviously not a good way to get better at tactics.
Similarly defensive puzzles and other puzzles where you have to calculate... just sit there and calculate. If you use up all your time, that's fine. The point is to get more practice. That's how you improve.
It would probably be good to play untimed puzzle rush and give yourself a time limit of 5 minutes per puzzle. Don't guess a move. Try to calculate the whole solution all the way to the end. If you solve it in 10 seconds that's fine, but after 5 minutes if you haven't solved it then make yourself move. If it took you that long it's obviously a pattern you're not used to, so it's better to fail it and study it after the session is over.
I grinded up to 2200 in tactics starting from having barely played chess before that. However, the reality is my rating in tactics was probably too high. Most puzzles above 1500 take me multiple minutes and I get the minimum 5 points. The only puzzles I ever get full points on are the endgame puzzles. No idea why these are rated so low. Below 2000 it is "trade the piece and take the opposition" or "calculate the square" and get the full 12 points.
I started donking around at puzzle rush and usually get in the low 20s (I always turbo move the first 10 puzzles and insta-quit if I miss as otherwise there is no chance of beating my last score, I am only counting runs where I actually fail three puzzles or run out of time). Within the first week or so I managed a 26, with the move to reach 27 on the mouse cursor as time ended, but in 2-3 weeks since then I have made no further progress in fact only getting 25 one other time, and I usually practice multiple hours a day in addition to practicing other aspects of chess.
I figured at worst I would memorize the patterns of the low-rated puzzles, which was my goal playing anyway since I feel like the low-rated puzzles are of the type I am more likely to spot in real chess games and may be more common as well. But I have noticed I actually have gotten worse at anything beyond the lowest level puzzles, often missing puzzles I solved in the past. The only improvements I have made have come from certain types of super-common puzzles at the low levels.
I review every puzzle I fail over 700 and it is usually three types: non-forcing moves, because I don't expect those on a puzzle with a low rating, defense puzzles, because these take to long to calculate and strategically in puzzle rush it is better to take a miss than do these, and coin flip puzzles where the rating is artificially low as guessing gets the puzzle right half the time yet calculation of the right move is hard. Anyway I would warn people that playing puzzle rush may not actually be a good way to get better at puzzle rush or maybe even chess tactics as instead of learning chess tactics you become conditioned to just guess at everything, so once you reach a score near your personal limit you will get no better.