I have made two over the years, one had Tee shirts of a uniform size so I ironed lightweight interfacing to each one and then cut each one to 16" squares, used a sashing of cotton. Hand sewed, not hand quilted around each square to hold in place. The owner is still using it.
The second one was made of shirts from a man's wife who died and they belonged to a Harley Davidson riding group, all different sizes and shapes of insignia so that one was a challenge.
I cut the insignias larger than I wanted, ironed on the interfacing, cut them to the size I wanted and then basted the pieces onto fabric in an orderly manner. Put the three layers of quilt together and used the blind stitch hemmer to fasten the three layers into one. The man cried when he saw it and paid me extra for my work. There were enough shirts to make him a lap robe and the quilt.
Tee shirts are not easy to work with but I wouldn't quilt over the painted surfaces, you would lose the effect. These are memory quilts and mean so much to the owners.
Carol J.