I suppose using a stretchy sock yarn is out of the question.
First, follow Jan's advice and don't tug on the floats, make them loose.
Then, can you add a few purls evenly space to make wide knit ribbing? Like a k5 p1 and just weave the unused color on sts 2 and 4 of the knits.
How about a fair isle pattern to use on the opposite side from the letters.
Unused color is 'X'
rnd 1: OOOXXOOXXOOXXOOO
rnd 2: OXXOOXXOOXXOOXXO
rnd 3: OOOXXOOXXOOXXOOO
or make your own pattern with graph paper or with Excel or other spreadsheet program.