1. You're not old.
2. Disclaimer. I’m not an expert, so feel free to take what I'm gonna say with a grain of salt. I’m pitching in because I think you and I have two things in common: we’re relatively small and both handle weights that are light in absolute terms. What I have observed during my own NLP might be helpful to you.
3. Form. A whacky form is a likely explanation for your below-average linear progress. I recommend you seek form checks, especially for the press and squat. The press is very sensitive to technique. A misaligned, poorly-timed, or misgrooved press won't go up unless it's light (i.e. not heavy enough for the purpose of training).
4. Using 1-lb jumps. For context, I did my NLP from December 2020 to June 2021, had a 2-month lay-off during the summer due to a move, and then resumed my NLP in August.
On the press, I started my NLP using 2.5-lb jumps until I failed to progress from 57.5 to 60 lbs, roughly 2 months into my NLP. On the next session, I reset the weight to 58 lbs and have been adding 1 lb per session ever since.
On the bench, I was wiser and made the switch from 2.5 to 1-lb jumps before I failed a set. I used the same approach when I resumed by NLP.
I have found that making the switch to 1-lb jumps works best when done a few pounds before stalling, so it has some room to work. In the case of the press, I am pretty sure I would have ended up in your situation had I not backed off a little. Perhaps that is what you need to do in order to resume a more typical NLP.
5. Frequency. As an ungifted presser, the most important lesson I have learned from my NLP is that both my press and bench are very sensitive to frequency in terms of days per week (not sessions per week).
In addition to the micro-loading, what worked best in driving progress on my press and bench during my NLP was to train every other day rather than 3 days per week: this would look like the 3C program (p. 304) performed on an every-other-day basis.
In my case though, I had a light squat day in my program at that point. So if you have recovery issues, this approach would look like the 3D program (p. 205) performed on an every-other-day basis.
Either way, both approaches would have you press 7 times per 2-week period, as opposed to 6. It doesn’t seem like much, but this is what “unleased” my progress on the upper-body lifts.
With the program you laid out, you would only press twice a week, which is less often than on a typical NLP. In my case, I am 100% sure this would have led to detraining. Even now that I am using the compressed TM for the upper-body lifts, I do it on a 4-day split where I press or bench every time I train, either every other day or 4 days per week.
6. Upper/lower splits. I have zero evidence to back up what I am about to say, but as a small person who handles weights that are light in absolute terms, I have found that the press and the bench are not stressful enough to elicit the SRA cycle when performed on their own.
I might sound a bit bodybuilder-like, but I see anabolism as a state. By state, I mean a systemic response rather than a localized phenomenon. Given that I don’t have a whole lot of upper body muscle mass, and that I press weights that are just not that heavy, I have found that an upper-body workout is not stressful enough to elicit a systemic response in my case. That’s why I stick with full-body workouts, so that my press and bench reap the benefits of the systemic response elicited by the squat and deadlift.
7. Practice. I doubt that using a compressed TM at this point of your training is a good idea. If I had done this at that point in my own training (back in February 2021), I am quite confident this would have led to regression rather than progress.
The weights you would handle on volume days would not be heavy enough to make that approach productive. Moreover, you'd get fewer reps on your intensity day, so less exposure to, and practice with, heavy weights.
This early into your NLP, it is important that you get frequent practice under heavy weights. Both pressing movements are very technique-dependent, especially the press: it's easy to get it right under lighter weights, but keeping the movement efficient under a heavy load is a sine qua none condition for progress on those lifts. This requires lots of practice.
Another thing to keep in mind is that pressing against a heavy weight is a skill of its own. You won't develop that skill while handling lighter weights for volume, or with fewer high-intensity reps. You're still fairly new to barbell training; you need to get used to putting up hard fights against gravity.
So in a nutshell, I think you should assess whether your form is an obstacle to your progress; maybe reset a tiny bit to give the 1-lb jump approach some room to work; maintain a pressing frequency of at least 3 days per week; stick with full-body workouts; and keep weights heavy on every pressing session.
Also, the guys are probably going to suggest you get your testosterone levels checked.