I was taught two different ways, both service related;
When I was in ROTC, the Ranger types would sweep that slide stop right up the side in their never ending quest to lower the disassembly, reassembly time in their constant challenging each other to do so.
When I was in Armorer School, they taught us how to insert the slide stop without doing that, and fast enough that the couple milliseconds wouldn't make a difference.
When one thinks about this; one the modern battle field, if there is time to take down your secondary arm, you should have plenty of time to reassemble it correctly, because you should have already maintained your primary arm. (the pistol is nobody's primary arm anymore, except staff officers.)
We did train to reassemble the M16A1 and the M60 fast, which makes more sense. We were also taught to quickly discover the cause of malfunctions (beyond SPORTS) and remedy them with minimal tools. (what could be carried in the Armorer kit. In the field, I actually broke it down to what I could fit in a 3 mag pouch. The rest went in my ruck. I used 2 qt. canteen covers for 7 mag pouches, carried on the sides.)
I use no frame cover, none is needed. If you have time to tape the side, or hold a credit card or whatever to it, you have time to insert it straight in.