If you're hitting 5" at 20yds you're doing pretty good!    

Bareshafting is one good tool for tuning.

After you fletch a couple try paper tuning the different spines.

You might learn a little more about your flight and be able to make a better informed decision of what to do next...

you can try them, but a 29" draw shooting fulll length shafts with that much point weight will probably be too weak. I'd go with 35/55's, and if you have to add a little more point weight. Use the brass inserts ,or .243 bullet epoxied behind the inserts, or the GT weights that can be added. Most likely a 100 grain brass insert, plus the 125 gr point should be about right.

wooden clothes pin to measure draw. clip it on the arrow and draw, repeat several time to get a accurate measurement

cool idea!

Has anyone heard of tuning the bareshaft to slightly weak because fletching will slightly stiffen the shaft? I just read that for the first time somewhere.

Its a common thing.

Depending on the bow you will be fine. Carbon recovers from paradox way faster than other arrow material and 99% of the people out there could get away with much weaker spined carbon and heavier points than they think. I myself am shooting a new mild R/D longbow that is 55#s at my draw and I am shooting a .600 spine carbon with 175 grain point weight cut to 29.5"s(I draw 28.5"s) and I am getting perfect flight. Throw most of what you have heard or read about carbons out the window and start experimenting with lighter spines and heavier heads and you will be amazed at what you will find. My go to bows are a RER Arroyo that is 54#s at my 28.5" draw and a Belcher riser with Border Hex-5 limbs and same weight and draw as the RER and I shoot 35/55s cut to 29.5"s with 190 grains up front and the flight is flawless. Try for yourself and see, most folks will be pleasantly surprised. Shawn