The number one piece of advice I have is you increase EITHER time OR effort, not both.
Specifically if you want to increase your trot time, then decrease the walk time. If you want to increase your ride time, add walk time. You are doing W27, T3 right now. To increase the trot to 5 minutes you might go W25, T5 or a more conservative W26, T4 first.
When I’m putting a horse back to work I will alternate between lengthening the ride and increasing the work intensity. For example I might walk 2 more minutes on Sunday, repeat the same routine on Monday and Wednesday, then convert two walk minutes to trot minutes on Thursday, and repeat that routine on Saturday. If I only managed three rides that week I would only increase the walk time, and do the walk time to trot time conversion on the next increase day. When I did only manage three rides in a week I typically didn’t do both increases in the following week.
Number two is to really learn your horse’s tells. Really focus on how he feels, how easily he moves, how willing to go forward, how much effort he’s expending. This will allow you to account for footing changes, slope changes, temperature changes, and so on. Walking in mud, even if not deep, is more work than walking the same track dry. Wet sand vs dry. Hot day vs cool day. Hacking out - up, down, obstacles, etc. As noted above, hand walk vs ridden. All will affect how hard your horse is working. If you tune in and learn the subtle signs of your horse getting tired then you will be able to stop before your set time for the day instead of inadvertently doing too much.
As it happens I am rehabing an injury right now, though it is cartilage rather than active tissue. I have an Equestic clip and I am referring to the analysis it is giving me very carefully. The symmetry analysis tells me which trot diagonal has a longer airtime, harder landing, and stronger push off. I’m primarily looking at how the landing and push off are trending after each ride. The clip also gives me the data on time spent in each gait, impulsion (in G forces) in each gait, and tempo (beats per minute) in each gait.
I can see that when I rode two days in a row and cantered the first day he was landing softer on the injured diagonal, and pushing more with the good diagonal. When I did two days of trot in a row (with no or well under a minute of canter) that trend didn’t happen. Yeah, I quit cantering for a bit and stuck to walk trot for a week or two before starting very brief bits of canter again.
The sort of measurements are far more subtle than a rider will notice - first day with canter is 3% heavier on the good diagonal, and the second day is 5% for example. I am really liking this level of detail. Without it I might have cantered for several more days before the uneven landing and push off became noticeable. Having the quick confirmation of my thinking the canter was the culprit (it could have been too much time for consecutive days) was very helpful too.
Our rehab has been out on the trails, fields and roads which meant my other app has been helpful as well in giving me time, speed, and distance (Caynax - non social media linked activity tracker) so I can see if he was slower or faster on the given day. A slower second day might suggest too much work the previous day.
Take it slow. Suspensory injuries are easily reinjured. It’s worth taking the time it takes. Good luck! 
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