Coming late to this thread but having played relays over 1M for 20+ years both in practice and philosophically
a) minimum hands with prime fits should be removed from the relay (because they are the hands on which opponents are most likely to interfere and sorting out relative strength/penalty intentions will be more difficult AND because you wish to put maximum pressure on opponents with a prime fit by going as high and fast as possible - hence descriptively as well)

hands which require a minimal degree of fit but no wastage opposite a shortage (typically with long minor/s) for slam are bad for relays as useful/key information comes too late
c) hands with game possibility and long suits or best competition are best shown early
d) long suits in relatively weak hands should be shown early.
Best of most worlds can be obtained by utilising transfers and fit-showing jumps, but you have to rid yourself of 2/1 mentality.
My current scheme:-
hence over 1S (5+S 10-15):-
1NT= relay (not 3+S unless 5+cover cards/16+HCP)
2C= transfer to D construct part OR Inv OR slam-try with short
2D= transfer to H see above
2H= 6+C see above
2S= nat const
2NT= limit or min GF with outside sing
3C= fit-showing with either C or H (limit or min GF)
3D= fit-showing but see above
3H= bal limit raise
3S= pre-emptive
3NT= bal (flat) min GF raise
4C= void D
4D= void H
4H= void C
4S= trad
To buy into the other argument about bidding over 1H opening: I originally used a 1NT relay to protect lead mainly but the loss of space and given the fact that I also pack more hands into my 1H opener (4+H may be canape in any suit but if longer S promises at least 5H) ensures that I use 1S as the relay but rebid NT to promise S - lessening the likelihood of playing there...
regards