Perfection on a budget? Hmmm...
The alignment jig provided with a Graham does let inexperienced users set things up easily and quickly, but it hardly approaches "perfection". I wouldn't call it "precise" either. Anyone who's aligned a Graham using a mirrored arc protractor will testify to improvements vs. the jig. If cost-effective "perfection" is the goal, the $110 Mint protractor will get you audibly closer with any (pivoting) tonearm, including a Graham.
As to sonics, friends and I A/B'd a 2.2 with a TriPlanar VII, Basis Vector I and all three Schroeders. This was on a two-arm table with Shelter, ZYX and Koetsu cartridges (same cart on each arm).
The 2.2 is among the very best for convenience, repeatability of setup and BQ, but with the above carts its sonic performance was lackluster when compared to those other arms.
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Jcarr mentioned headshells with drop down sides. I don't believe any TriPlanar has had those since at least 1983. The Mk III did not, nor did the Mk IV, VI or any version of the current Mk VII.
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A used TriPlanar Mk VII would be above the OP's $2K budget, but a Mk VI (if he can find one) might go for that or a bit less. It can even be upgraded to Mk VII by that friend of Ralph's when funds permit. Of course by the time a VI shows up, he may have saved enough for a used VII! :-)
A used Basis Vector should fit the budget. VTA on the fly is a challenge and VTF/azimuth adjustment interact, making fine tuning a chore. Solid, good sounding arm though.
Depending on the turntable, Chris Brady's add-on VTA adjuster is very well built, easy to use if you have access beneath the armboard and provides precise, on-the-fly height adjustment and repeatability. It could make many tonearms lacking this feature eligible for consideration under the OP's criteria.
Friendship disclaimers (so Dertonarm won't yell at me):
Dung Tri Mai
Frank Schroeder
Not Bob Graham or A. J. Conti, but only because we've never met except online. Otherwise I'd disclose them too!