Is the wiring inside your new QTH in conduits?
No - residential codes here do not require conduit routing except in steel-framed homes (very few of those around these parts).
I also suspect that the hot or neutral wires are at a 1/4 wavelength (or multiple thereof) of 40M between the main box & the various power outlets. GFI's trip for an unbalanced current flow between the hot & neutral lines. So, it possible for the neutral to be a suspect as well.
Does this happen on other bands?
160-10. No worse or better on any band. It is quite simple - the higher the SWR, the less power it takes to trip the breaker.
I would NOT add ferrite beads to any ground wires! You may need the lack of reactance there. I second using strips instead of wire for the rig ground, also to eliminate resonance issues.
Is your power line house feed come in above ground? If so, that could also be the RF entry point. Toroids on both hots there may help.
I've got more braid on order, along with a bunch more toroid chokes to be placed on the RG-8X feedline. When the braid arrives I will be installing a more effective RF ground, with multiple rods. A local electrician also suggested placing toroid chokes on the AC power cords here in the shack - that might be some help, too.
The power drop to the house is underground with a minimum depth of 24", as is the neighborhood power distribution, so that is not likely to be an RF pickup problem.