The front mount chucks are a bit more forgiving to dial in runout to the backplate, BUT, more details to discuss here. My original Bison integrated (non-SetTru) 5C actually wasn't all that great, about 0.0015" TIR. I cant recall what the factory specs were but I wanted better. And that TIR was on a preferential D1-pin orientation (which you should always repeat). That's the end of the trail for a direct mount chuck. You cannot (easily) disassemble an integrated chuck even though seeing 3 front screws might lead you to believe that. They are factory pressed & gronked.
If you get a plain back 5C chuck designed to mount to variety of backplates like some of the Asian models, you might be able to use this to your advantage. As long as the face lip / mount is not too tight you could shift the chuck to null runout & lock it in place. The issue is, it really SHOULD be a snug fit or its probably going to drift eventually. Maybe if you are brave, turn off 0.002" from the backplate boss & insert shims onto the quadrants. Like 0.0030" at 12:00 & 0.005" at 6:00 gets you 0.0025" net displacement. That kind of thing. Tune-able to 2 axis.
Now none of this speaks to the 5C taper collet face. If the chuck arguably runs true to spindle center but the seat is ground slightly eccentric, its still going to have problems. Thats why I like to put an indicator directly on the seat to get confirmation. Adding a questionable collet + questionable dowel is further aggravating the issue, so have to do this step by step
