How do you determine what 'level ground' is at the moment? It would feel the same as being on a slight hill in the RE model...
That's because you would be on slight hill neither on re or fe model. If you stand on tilted surface the strenght of gravity will not change only its direction compared to the angle of surface you are standing on. You could still easily measure the real strenght of gravity simply by measuring the direction where it is strongest. And measuring the streght of the gravity to that direction.
Also the moon/sun gravity theory does no work because they move but low/high gravity areas do not.
Alternatively, if you allow gravitation in the FE model then the differences can be explained in the conventional manner (local mass/altitude variation etc...)
Yes if you would allow that there would be no problem. But the faq says that earth has no gravity.