Wow, that's a lot of volume
Doing 5x5 overhead press and 5x5 bench press is a lot for one day. Doing that, and 5x5 rows, AND three sets of 15 pull-ups is doggone impressive. Even if your pressing weights are puny, that's quite a lot of work. If you can do it, awesome.
My inclination is to lower the volume and make your A and B days more distinct. I'd use a primary movement in each, an assistance movement for the non-primary movement, and a handful of prehab exercises to keep the shoulders happy. Perhaps something like this:
_____________ A ____________|____________ B ______________
| Overhead Press 3x5 | Bench Press 3x5 |
| Pull Ups/Chin-Ups: 3 sets | Bentover barbell row 3x5 |
| Push-ups: 3 sets | Handstand work |
| Dips: 3 sets | Inverted Row: 3 sets |
| Prehab Grab Bag: Cuban presses, band pull-aparts |
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Another way to write this would be:
_____________ A _____________|____________ B _______________
| Barbell overhead push | Barbell horizontal push |
| Bodyweight vertical pull | Barbell horizontal pull |
| Bodyweight horizontal push | Bodyweight overhead push |
| Bodyweight downward push | Bodyweight horizontal pull |
| Light multi-directional work |
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Handstand work depends on your shoulder mobility and strength. It could range from inclined (pike) push-ups to handstand holds to full handstand push-ups.
I altered the order of the workout because I like alternating between movements. Doing overhead press then push-ups burns me out, but overhead press then chin-ups then push-ups is much easier.
If it isn't contraindicated by your leg issues, you might do three sets of strict presses, then two sets of push presses for explosive power work that overloads your press. If the push-ups don't challenge you, do clapping or wide or one-handed variations.
I wouldn't be worried about rest days being messed up by a stretching session. I find that my recovery is aided, not hampered, by a ten-minute warm-up and stretching routine in the morning or on rest days. Going for walks helps too. If you are concerned about ab work interfering with recovery during rest days, then reducing the volume as I've outlined should make it possible to put ab work on workout days.
My similar routine
I'm in a similar situation, being barred from squats and deadlifts for a time. But I'm also barred from barbell pressing as well. Here's what I'm doing:
_____________ A _____________
| Pull-ups: 3 sets
| Dips: 3 sets
| Band pull-aparts: 1 set of 10 for each kind
| Inverted rows: 3 sets
I progress by doing three sets of a number of reps that is moderately challenging. Once it becomes easy, I add one. I do not go to failure.
In the beginning I did five sets because my dips and pull-ups were too weak to get enough volume into each set. Now I find it counterproductive to do a ton of upper-body volume all on one day.