Yes, that's a real problem - and I think those "arbitrary values" even vary by manufacturer. The best strategy I can come up with right now is ordering a pair of contact lenses based on a "best guess", possibly by an optician, based on your values for glasses.

Then, check whether they are over- or under-correcting and order another pair with slightly different values under the assumption that your initial "best guess" was off. Then, compare and repeat..