Well, if you decide to stick with 5/3/1, I would definitely recommend lowering your TM if you are experiencing a drop-off in strength as you shed fat, especially if you are having joint issues. I can't see how 5/3/1 with an out-of-date TM would be a good idea.
You may want to consider other programs if you really want to attack it with everything you have. This one has caught my eye before, and I may give it a go next summer.
FWIW, I am in the same boat as you (6'00", 291 yesterday, minus the injuries/ailments), running 5/3/1 and prioritizing strength. My current lifting numbers are a little bit higher than your pre-fat loss lifting numbers. I'm not a dieting ace by any means, but I've managed to slowly shed a lot of fat while getting stronger over the last year and a half. Starting point was around 330, with zero lifting experience.
SLOWLY is the word here. Unless you are a very good dieter and lifter, you have to be able to live with that if you want to shed fat and keep or build strength. It is a long ass road, no doubt about it.
Do whatever keeps you engaged and moving in a good direction. Don't ever quit.
I have looked at that program before and disliked the lack of volume. Lack of volume maybe what I need though.