Question then: did you try doing the exact same program you're doing now with good form? Before, I bet you had a sporadic program that didn't utilize the reps and sets schemes from the hundredpushups.com manual. I believe you might be associated your gains inappropriately with bad for rather than the initiation of a structured program.
I followed the website program intitially 3x/week but the problem was that I was doing this with what spare time I had left at the gym on my lifting days... I didn't wanted to do it first because I didn't want it to affect my lifts[specifically the bench pressing] so this was just a challenge I decided to take on after the lifts. I chose to throw it in there because I always had a bit of time left during my hour and didn't want to split it up into another session later in the day or do it on my off day from lifting. So already the bench pressing may have affected my ability to do them since I'm sort of working on "leftovers". I'm telling you this as a disclosure so that you could take that for what it is in determining what may or may not be the issue but I'm still doing that now[doing pushups after my lifts] with my current variation.
Anyway, it's so long ago so I can't remember when I stopped but I think I stuck with the websites program for a couple months doing their initial test and following their weekly program but it should be quite obvious now that I was lagging behind since the program is 6 weeks and I took about 8 and I repeated some weeks. The main problem was that the last set everytime was a test of max with the initial 4 sets a % amount under your intital test. My initial test was like 21 but really it was like 19 if you count only the good ones. So week one I would do[looking at the website now] 14, 14, 10, 10, max[at least 15], except that wasn't the case, the last set I could do like 13 since I'm doing multiple sets and getting gassed whereas my intital test was just one set of what I could do tops. So I would do week 1 again until I could hit the min of 15 on my last set. After 2 months, I was by comparison still around the beginning of week 4 level. 21, 25, 21, 21, max[at least 32], I did 30 max.
It was then clear to me also that I was taking longer rests between sets and getting back to work later and later since I was beginning to go over an hour. One day by happenstance, the gym had a pushup challenge. The number to beat was 56 or something so I wasn't going to bother since I knew I couldn't. I was walking by as a trainer was about to begin the count for someone taking it on. He was doing half assed ones and the trainer was still counting them which was BS and he punched out 57 just to beat the record. I was like, fuck that, I can do that. I got in line and did like 72 which put me on the board[which someone beat later that day]. The burn felt different because I was still able to bang them out since I didn't have to lock out. So it just sorta clicked, the next week I decided to try something different, do 4x30's[non lockout] with no test of max on the last set and the goal was try to increase by 5/week and on occasion I would take a day off to test with perfect form pushups. The intial 2 sets were cake but the following 2 was where I struggled but I was able to complete. Some weeks I still repeat but now I'm doing 4x70-75 and as of the last test, I did about 68 full lockouts.
Also, squats and bench press are low risk lifts with good form. I have no idea where you got this idea that you are likely to cause serious injury to yourself. You are more likely to hurt yourself doing crappy formed pushups than relatively good formed squats. On top of that, women are just doing a substitution movement. It's like people lowering the weight on the bench press. If they are utilizing their upper body, going through a full ROM, and minding all other important form points, they will be doing the same movement, just at a lighter weight. The analogy doesn't quite apply right.
This is a different beast altogether... to me, an exercise under a load[barbell or what have you] is nothing to mess with so I do work with only good form[that is I don't take shortcuts and also why I suck at squats]. I know my analogy wasn't spot on but the point was that non full lockout pushups to me doesn't "feel" like it's injury prone when I do them... I'm not buckling at any point, I feel pretty solid doing them. If my body told me differently, then I wouldn't be defending my case here today.
edited for clarity