FBinNY 

The "right" solution is spokes that are the right length, and loading tension in a way that avoids then high/low phenomenon.

That said, your approach using washers creates more problems that it solves.
1- nipples have hemsipherical (or conical) heads so they can comfortably sit at an angle to follow the line of the spokes (side to side, forward to back). You probably will have a very tough time finding washers strong enough not to split, and/or which won't induce high local stresses on the rim.
2- the taller nipple height will make it harder to protect tubes from hyperstretching at the steps each high nipple creates. It's a recipe for chronic rim side flats.
3- You'll need as much rim depth as possible to mount tires. Odds are that there simply isn't enough depth or side clearance between the tire seats, and mounting tires will be a bear (it already is on many rims).

So, back to what you don't like. Spokes that come up beyond the top of the nipple. As long is it's not enough to cause running out of thread (test a spoke and nipple off the bike), it's easily remedied with a fast pass on a narrow grinding wheel. This has been SOP for well over half a century and there were even special 8mm grinding wheels made specifically for this job.

So those are the considerations, and it's now in your hands.