At what dsitance from the bow should the unrigged hull balance fore and aft?

Root around in the search feature and you may find an answer to your question. If so it will be a general answer because there are subtle
differences in in hulls that will change the dimension somewhat.

The best thing to do is to cobble a test tank together. You can make it from plywood sheathing as used in roof decks and elsewhere. (cheap)[:)] Your profile says that you are from Marco Island. Right now (after the recent Hurricane) you can probably find some material in the junk heap. (cheaper still)[:D]

Most of the EC12 sailors set the boat up for a bow high attitude of somewhere between one half and two degrees. They'll add ballast in the aft section to induce the higher angle when sailing in heavier air. Ain't no way to do this with a tape measure. Build a tank, it's easy and inexpensive. You are welcome to use my tank if you like. It's a pretty good drive from Marco to Lakeland (FL) but the offer is there.