Hi Shails,
Could you provide any pictures and details of your setup?
If the tail is dropping in a upright hover and the nose is dropping when inverted it would suggest that there is something else causing this, as in a tail heavy situation when inverted the tail would continue to drop as in the upright hover situation.
If anything it sounds like you have a small amount of rear elevator cyclic offset in your swashplate, as this would explain the tail dipping when in an upright hover and also explain the nose dropping when inverted.
Couple of things i would check:
Firstly, has the machine been crashed recently? If so then check the central elevator bellcrank arm (610-226), as in a crash this can be damahed and it can move on the pivot shaft. Next, I would check the mechanical setup just to make sure that there is no rear elevator cyclic. A good swash level tool like the Trueblood or FBL Rotors swash tool makes checking this a simple and accurate job. Even if the swash looks level it could be very slightly off and this could cause the problem your experiencing.
Hope this helps and let us know how you go,
Cheers
Ross