I am not sure of the variations that I get with the loading controls during western blot. Is there any other proteins than beta actin which have been used stably now with you?
in my experience you can always use core histone proteins for that purpose unless you do prior fractionation or lyse the cells/tissue in a way that removes chromatin fraction from the resultant sample. Total H3 and H2A levels are excellent loading controls especially because the Ab against them (e.g. made by Cell Signaling or AbCam) are highly sensitive and do virtually do not create non-specific background. Just collect media, spin down, resuspend pellet/cells in a Lysis buffer, sonicate briefly and apply onto gradient gel (4-20% or 4-15% TG or Bis-Tris).
Not specific to trophoblastic tumor but have you tried TATA binding protein? I use routinely for my nucleoprotein loading control (prostate cell lines).
Did you ever check the protein amount that you are loading if it is equal or not? I am working with HTR-8/SVneo cells, so these are trophoblastic cells and I never faced a problem by using beta-actin. But finally this depends on the question you're working on or which pathways you affect during your cell treatment.
GAPDH would be a very classical protein people are generally using in research.