Can First Win of the Day give some BE as well?
The bottleneck of BE is to the point where you can't buy anything above 1350 from the actual champion shop since you'll never have any BE to do so; you have to hope for RNG to give you a good shard, in which you still have to pay about half of the cost of the champion (which is like 3-4 levels' worth for a 3150 champion). Giving level-based (maybe) BE for FWotD would help everyone out and compensate for the lack of BE upon the end of a match.
Maybe 100 + (level-30) * 5 BE and lower the XP to 400-500?