As some commenters have already suggested that there is no basis for this theory, and as nothing has come forth after some time has passed, I thought it would be worth examining your points critically to see if the theory holds any weight at all, or if alternative explanations might be more plausible, as a frame-challenge.
The wall art in the Under Gallery included some TARDIS-interior roundel style visuals.
It could be just that - "wall art". And it wouldn't be the only Timelord art on display in the gallery.
The Under Gallery curator is VERY heavily hinted to be a future incarnation of The Doctor.
That much is true. In fact, it is more than hinted at if you look at the extended universe. I'm told the novelisation of Day of The Doctor confirms it too. But if the buildings are his TARDIS then presumably he travelled there in it, in which case The Doctor must have invited UNIT to set up in it rather than UNIT creating the space, which flies in the face of your next point that Kate doesn't know who The Curator is.
None of UNIT staff seem to notice the very obvious facial similarity, not even Kate, assuming they meet (possibly similar kind of mental interference as in the Black Archive).
Well, they wouldn't. Tom Baker, as he is now, is barely recognisable from his younger days playing The Doctor. In-universe, the 4th Doctor never aged that far before his regeneration.
The buildings are only 3.6 Km apart and the TARDIS interior has been described as rather large previously.
I don't really get this part of your theory - are you suggesting that the two buildings are the same space, spanning the 3.6km distance between them? If so, you're describing something that is big on the inside AND big on the outside. That isn't what a TARDIS is.
Also, if they are the same space (ie a TARDIS) they still have different entrances. I don't know of any TARDIS which has two entrances. Although dimensional transcendentalism is a bit of a constantly unravelling mystery, the way I understand it is that the TARDIS maintains both the interior and exterior dimensions (in 'Flatline' the exterior shrunk while the interior remained the same). Having two entrances to the same space would require the TARDIS to maintain an exterior that matched the interior, defeating the whole object of fitting a big space inside a smaller space.
If you meant that the two locations are two individual TARDISes then it begs the question where the other one came from. Assuming The Doctor fixed the chameleon circuit on his own then he'd have to have obtained at least one other, otherwise, he's got his hands on two new working ones. Also in this case, their being 3.6km apart adds no weight to the theory, as two TARDISes could be right next to each other and still be massive inside.
Kate claimed the TARDIS couldn't land in the Black Archive. Very few circumstances can block a TARDIS from landing, but landing inside (a much more experienced version of) itself is likely one of them. And indeed the Doctor tried and failed to land the TARDIS there.
The Doctor was also previously unaware of both spaces, so perhaps the inference is that he had never been to either of them because they had deliberately been made TARDIS-proof?
Both locations contained alien artefacts, including at least one Vortex Manipulator which we know can emit artron energy and can interfere with TARDIS navigation (as demonstrated in Rosa). Perhaps this, and other artefacts contained therein are what prevent the TARDIS from entering?
But also - we have to take what she said at complete face-value, which is that the TARDIS cannot land there. It clearly has no problem actually being in the under-gallery because, as the final scenes of Day of the Doctor show, all three TARDISes are sitting there as the Doctors exit one-by-one. The Twelfth Doctor's TARDIS is still right behind him as he has the conversation with the Curator in front of those beautiful roundels. No explanation is given as to how the three TARDISes got there - perhaps UNIT physically moved them there, as they moved Twelve's at the beginning of the episode? In any case, they have no problem operating and leaving from there, so perhaps it is just locking on to it as a destination that is not permitted?
As stated, this isn't meant to rip your theory to shreds, but just to provide a frame-challenge and alternate theories.