[Nitram Draw]

You could also try to fight in nebulas, shield aren't as effective.
Fighting a war of attrition against a maintenance free opponent isn't a good idea IMO. You will lose units also and still pay to maintain your remaining ships.
A better goal would be to cripple his shipbuilding capacity, either by targeting planets with yards or big resource producing/storage planets. Once he has built them he's done. Keep him from building as fast as you and the attrition strategy makes more sense.
The benefit of the Wave Motion Gun is range and a +30 to hit modifier on the weapon. This makes those long range hits more likely, although I agree sometimes I'd rather fire 4-5 beams every turn. WMG's are a good alternative to going toe to toe.