Should I upgrade my phono linestage first or the tonearm for better results?

Sure there are diminishing returns but in the context of a six figure system and if you can afford a $10K cart then the Phantom could take it! I’m surely not recommending it as a next step and I’d assume you have upgraded the phono stage commensurately before then. 

My own experience was that only once I upgraded my arm (TriPlanar VII replaced by a Kairos) was it that I really found out what my cartridge (AirTight PC1) could do

Upgrade both very soon for best sound.

Off your main question but if you really have money burning a hole in your pocket you should invest in some proper power cords ( you didn't list any power products)

personally I like Synergistic Research but there are lots of good options out there all easily available used and if you haven't done so you really should invest

" I have just ordered a Mint LP protractor kit, it is arriving next week. I am looking forward to more precise alignment than the DB protractor I currently use."

I think you'll be more than pleased with this purchase, and this may end your desire to throw cash at a problem that may or may not exist.  Going from the DB to the Mint is a major leap in setup precision - orders of magnitude, not degree.   Frankly, I'm always stunned when I hear folks with nice systems not using an arc protractor to do their setup.  

I can’t offer any knowledgeable comments about your tonearm, but I don’t doubt that Folkfreak has provided you with some good thoughts. Regarding the phono stage, though, my strong suspicion is that it is not doing justice to your fine cartridge.

A major reason I say that is what I would consider to be the AcousTech’s absurdly high 10,000 pf input capacitance in moving coil mode, together with its fixed 100 ohm load resistance (which I suspect is necessitated by the very high input capacitance). For further explanation see the post by Lyra cartridge designer Jonathan Carr (JCarr at Audiogon) dated 8-14-2010 in this thread. And keep in mind that he is referring to capacitances as low as tens of pf, not ten thousand.

My suspicion, btw, is that the reason such a high input capacitance value was used is that it is serving as an inexpensive way of avoiding what would otherwise be issues in the design.

You may want to consider the Herron VTPH-2, at $3650 new. If you research past threads here and elsewhere, you’ll find nearly unanimous glowing praise from all who own it or have heard it (including me), as well as for Keith Herron as a wonderful person to deal with. Some other owners have reported finding it to be competitive with $10K phono stages. It has only unbalanced inputs and outputs, but I don’t see that as being an issue with your BAT preamp.

Good luck. Regards,
-- Al