tonearm issue

It's something, patience and good methods are needed.

Back to basics, you need to check/re-check everything. I use several levels simultaneously (check that they agree with each other first, some are a speck off)

mine and friend's TTs

I once found a platter that was not properly seated on the spindle. off/on, done

I once found a TT that was sitting in a plinth, unfastened, another: one screw of 3 tight, the other two snug but not tight. An arm not really tight on the arm board, mechanic's elderly father forgot to tighten the wheel nuts om my wife's MGB, 

recently found two removable headshells not perfectly parallel with the tonearm, put little 10mm diameter bubble levels on the headshell, and acrylic block with lines behind the headshell, not the arm for VTA

adjustable feet to level the plinth, I shake rattle and roll them to see if they settle different than they just were, and re-check after a few days.

differently (sorry Mrs. Carter, ma'am)

You might want to simply level the whole suspension, Those springs are pretty loose and doing shipping will bounce around substantially. 

I have my suspicions, but frankly, I'd start from scratch.

1. Carefully investigate the tonearm wiring. Ensure there's no binding or pulling in any way shape or form. In fact, you might disconnect/remove the cartridge to help with this process. Only when you are 100% sure the wiring is up to snuff, remount/reconnect the cartridge.

2. Relevel everything. If the feet are adjustable, start by turning them all the way into the plinth. Check the level. Then slowly, slowly unscrew the feet, raising the plinth until it is dead level. Check and recheck. (OH! I hope you started on a level table or surface, yes?) 

3, Relevel the suspension. Put the bubble close to the spindle as possible. Even better get one of those records weights with a bubble level built in. 

4. I'm making a huge assumption here that you've correctly mounted the tonearm but check THAT mount to make sure it is level as well.

Once all that is done I think you can safely eliminate the TT as the problem. 

NOW you can focus on the tonearm. You say they worked on the arm lift mechanism? Make sure nothing else was knocked off kilter, the weights? Perhaps a bearing? Make sure you have a bright light to assist. Gently, carefully make sure the arm can freely move in all directions.

Now, zero out the antiskate. Gently set the needle on a non-spinning LP. (Use something you don't mind scratching, just in case.) That needle should not move. Period. Start the turntable and see what happens. The needle should track. 

What a lot of people don't realize is that "skating" happens as the mass of the cart and tonearm gain momentum as the arm moves towards the center of the record. Anti-skate is supposed to provide JUST enough pressure outwards to keep that from happening. My suspicion here is that somehow either the anti-skate mechanism has been compromised or a bearing is out of whack.

Good luck and let us know how it goes.

Happy listening.

Lots of great advice here, both on TT set-up  and on Cart parameters.

One small contribution - I suggest getting two or three CLEAN, OLD LPs to use until you have satisfactorily installed the TT and Cart.

They will be fine for your purposes and save you from possible a possible 'damit' moment...

Good luck