The factors that trigger change in metabolism from weight lifting, as opposed to change in strength, are the exercise momentarily driving cellular energy reserves extremely low (specifically, the cell senses levels of AMP, which become high as ATP and ADP are exhausted), from the cells becoming hypoxic (very low oxygen), and from occluded blood flow.
All of which occur in the kinds of training mentioned above, and which do not occur in powerlifting or strength style training.
This partly is why powerlifters tend, most of the time, to look like powerlifters. You’re training in a way that helps look like a powerlifter, not like for example a sprinter, or a bodybuilder who trains as mentioned above.
Thibaudeau’s fat burning training methods are in many articles on the site. Vince Gironda’s training out there a lot on the Web but I don’t have particular links. For example though, his 8x8 training is 8 sets of 8 reps, with no more than 30 seconds rest between sets and more preferably working down to more like 15-20 seconds, AND (importantly) with the reps done relatively slowly both up and down, with constant tension on the muscles. How much weight is used? About half of what you’d usually use for 8 reps!
That’s just one way. But typical strength training, the cells are not exhausted at the ends of sets, there was little occlusion of blood flow, and no hypoxia generated.
There are many articles on high intensity interval training as well. This could be sprinting, or sled pushing, or could be weights with routines such as Tabata.
I would disagree that it’s fundamentally a nutrition problem now, unless I’ve misunderstood your nutrition. Any number of people would lose fat on your present nutrition and at your lean body mass, if your bodyfat percentage figure is correct. You were doing so yourself before. So it’s a question of your body’s setpoint: it is resisting losing further fat. To resume losing fat, that set point issue will need to be addressed, and one of the ways I would do that is with training that’s proven to shift the body’s metabolism towards fat loss, rather than training which is in no way optimized to upregulating fat burning.
It’s true that adding muscle aids in burning fat, but how rapidly are you adding muscle with this routine? You’ve seen your recent results. StrongLifts does not employ the training techniques that change the metabolism towards burning fat probably because that was never a goal of the program, and certainly isn’t the main point of it.