ericgibbs,
There's an error in your transformer model. You set the secondary resistance to 28Ω, so no wonder the voltage drop was too high.
I tried setting the primary and secondary resistances to 30Ω and 1Ω respectively but it made the simulation too slow so I've included separate resistors to model it.
To ensure the relay turns on, the series resistor should be 33R or 27R and must be rated to 2W.
It will be fine even with 470µF for the filter capacitor (providing you don't connect any larger loads to it) but there's no harm in it being 1000µF.