white termites - 2 orange oil treatments, building won't fumigate
What the heck are they...?

Those look very much like Western Drywood Termites

If I can't fumigate, what are my options?

Spot treatments do work, and there are several types of spot treatment (local poisoning, freezing, electrocution...). Effectiveness is variable and depends on ability to locate the termite galleries and nest. If it were me I would start my own search for &quot;kick-out&quot; holes (the little holes that are used for termites to eject frass from their galleries) and use consumer termite poison liberally to start killing them off. probing with a thin awl can help you find galleries.
Fumigation (or other &quot;whole house&quot; treatment; there is a method to heat up the structure and &quot;cook&quot; them, also) is truly the only way to ensure that all have been killed.