.... Or .... your kit is fine, leave it alone and just go out and shoot. Do you have a speedlite? you might want to think about lighting as this is a cheaper and better way to reduce noise and improve overall IQ. Seriously , even just a $20 reflector can improve your outdoor portraits.
For candid low light shots you have the 50mm 1.8 which works just fine, I had one for a few years and it served me well (kinda miss it now!). I use my EOS M now but that's a diff topic ...
Going FF alone is not the answer. So, you are willing to spend about $1500 on a 6D and $2000 on another lens just so you can get "cleaner images"?
Sure the 7D can be noisy over ISO 1600 but are you missing a lot of shots because you can't use ISO 6400? Hmmm, I don't think many people use that for portraits anyway. (I could be wrong, I'm sure someone will come on here and prove me wrong!)
I was close to buying a 6D for a similar reason to you and had to just slap myself and say "shut the hell up and just use what you have". I've decided not to buy any more gear this year and to try and improve my technique and lighting skills. Two things that will improve IQ!
Then again who am I to object! Do what you like!