Ben,
If I may be so bold as to opine--ok, this may peeve some people off, but don't "settle" for what you've got here. You've admitted that it wasn't what you were going for, and that you made some mistakes, so take the time and have the energy to try to achieve what you initially were going for. You can learn a LOT by correcting a mistake--I've been there plenty of times, and if you settle for what you've got, you're missing a golden opportunity to really "rise up" here!
Remember that "white is white". It's going to look "white". However, you can tone it down with a light wash of dark umber, or even tint the next coat of whitewash with a TINY drop of buff or even brown. And I mean "TINY"!
Personally, I'd go for just doing it straight; then wash it lightly in raw/dark umber after it's done, and then you can still add in even further graduations of white with a brush using either oils or thinned acrylics.
GO FOR IT!!!