Hey, everyone! I am new to this forum, but I think I could say something about this one.
I think instead of switching hands after every stroke it would be better, in your case, if you use the same hand to stroke several times while keeping the other hand at the base such that the index finger is below the shaft pressed against the part the scrotum where it attaches to the base of the shaft (or slightly below it), thus holding the scrotum back and preventing pinching when you initiate another stroke. At the same time you can use the thumb of the stationary hand (which would be on the dorsal side of the shaft near the base) to keep your shaft skin, on the dorsal side, from sliding towards the glans when you stroke. Once you have made several strokes with the same hand, switch hands, and do the same.
I guess this pinching thing would be a problem even for those with bigger penises too, if they have a turkey-neck, right?