Any suggestions on how best to measure 5/8 ounce?

A digital scale is always handy to have around the kitchen. You can usually find them for about $15.

1 1/4 tablespoons will get you what you want. There are 2 tablespoons of liquid per ounce, for future reference. Convert your measure, in this case 5/8 to a decimal, and multiply that by 2- so .625 x 2- and you get the answer, 1.25, which translates to 1 1/4 tablespoons.