I am no help with colors, but I will advise you to prime the oil painted fixtures before painting them with latex paint. I once lived in a house with all oil painted walls. Back then, you had to prime them with oil-based primer to switch to latex paint, or the latex would simply peel off in time. Since I could not breathe oil paint fumes, there was no way for us to paint the house interior! Nowadays, I believe that latex primer will do the trick.

So I would want the walls to still be an off white with enough contrast to make the Alabaster trim to still pop and look like the cleaner white. Alabaster has a Chroma value of 0.66. Which means there's going to be a very short list "off-white" wall colors to go with Alabaster trim The rule of thumb to make a color of white look like the cleaner white is to pair it with a color that has a Chroma value 0.20 more or less than. From this list, PPG's Delicate White, Chroma 0.38, is a good option. Sherwin-Williams' "match" to Delicate White is good.

The trim is semi gloss. For a bathroom, would the sateen finish work and still give enough contrast to the semi gloss?

I would probably do a white cabinet. I would like to paint my walls and trim in alabaster, can you please send a pic of your wall with the trim? Would love to see it before I commit!