An interesting idea, but those caps are just too high for what you're proposing. Speedruns will still be easy, especially for the Brayflox tier. Below 50 dungeons cap you at 2-3 character levels above the level requirement. Given that a gear level isn't exactly equivalent to a character level, I think setting the cap to be exactly 10 iLvls above the minimum requirement would make more sense, ie.

AK and WP: 55(from 45)
Copperbell, Hawkke, Pharos: 60(from 50)
Brayflox, Halatali, Lost City: 65(from 55)

*I accept ridicule if I actually got the base iLvl minimums wrong

Those caps would probably shut down speedruns pretty quickly, but lots of people wouldn't want to run these period because what's the point of having all this awesome i100+ gear if Coil is literally the only place it can be used?

But here's an idea: Don't iLvl sync to some arbitrary number. iLvl sync to the tank. If you've got a high level tank, that's all fine and dandy and you can choose what to do. Come in with an i55 tank and the DPS will no longer be capable of stealing hate just by looking at something and they certainly won't push for a speedrun. This may push Speedruns back to the Party Finder, where it arguably belongs, instead of having the expectation prevalent in the Duty Finder.