I've never learned how to post pics in a thread, sorry. I will say that it sounds like you are MUCH more meticulous than I am when it comes to knot tying!! So I would guess your knots are much prettier than mine. I also have trouble getting the 12#-15# fluorocarbon to cinch down easily which is why I only use 5 wraps on the Trilene knot. More wraps than 5 and I really struggle when cinching down. Is this because the fluoro is stiffer than mono? Probably. I cinch slowly and with saliva as lubricant, and also use my fingers to push the knot down. The only time I tie it again is if the fluorocarbon is noticeably stretched out and shiny above the knot like I "burned" it when cinching. I also leave a longer tag end of about 1/4". I'm not fishing weeds so no worries about a longer tag end grabbing them.
So assuming you tie better knots than I do, but I don't break off on hooksets, something else is different between us. As I stated in an earlier post, 51 weeks a year I'm fishing ML or M powered rods with 8#-10# fluorocarbon mainline and leaders. But 1 week a year I use a MH powered rod with 12#-15# fluorocarbon mainline to fish ledges with jigs and soft plastics. Lines I've used are Seaguar 12# & 15# Invizx and 15# Abrazx. The only fluorocarbon I experienced break-offs with on the hookset was Berkley 15# Vanish.
I feel like I set the hook hard but maybe not as hard as you do? Also I'm using a Loomis MH (3-power) which may not be as powerful as other manufacturer's, so maybe your MH rod has more power?
Have you considered ditching the fluorocarbon and using straight braid?