Tonearm for Technics 1200GR

So, when looking for a new arm, the p/s should be less than or equal to 225mm. So if the SME is 233.2 mm the the new armboard would need to adjust, is some direction away from the spindle, 8.2mm. 

Is is this generally correct?

You can look at the arm from the top to figure out how much the new arm can be moved within the armboard area. If it’s too far then maybe it will be impossible to use dust cover, counterweight can be out of the Technics plinth. So it depends on each particular arm. Some of them are way different with armtower like Reed or TriPlanar. You can look for the Reed 9’5 (used/demo) maybe ? Great new arm!

Some nice vintage 9’5 arms can be mounted easily, like SONY PUA-7 stand alone version (very nice tonearm). Not cheaper version from Sony turntable, but a version that was sold separately, compare two different version of SONY PUA-7. This arm is fully adjustable, top quality, with the best armlift ever, VTA on the fly. Highly recommended! The price is lower than your limit.

You should first look at adding isolation to the turntable before anything else. That’s the weakness in the SL-1200 series. Your arm is more than up to task. Second area of improvement is in the cartridge. 

I do have an isolation base. And I’m on concrete so that typically helps too. 

I am just curious why you feel the need to replace the stock tonearm, insofar as the ones you are considering are not obviously superior to the original. Also, you say you must have an armboard available for purchase. Lots of luck with finding a ready-made product to suit.

If you choose a tonearm with a similar pivot to spindle distance to the OEM tonearm, and if the diameter of the vertical shaft that must mate with the armboard is in the same ballpark and can fit through the existing hole, then you may not need an armboard. But these requirements will dramatically limit your choices, if you feel you must go ahead with the replacement process. Instead, you can buy a slab of brass or aluminum (two materials I recommend for the job), have it cut to size by a machinist (just remove the OEM armboard and measure it, to determine the needed length and width and where screw holes need to go, etc.), and then have it drilled exactly where you want to locate the pivot with a hole that is exactly the proper size (by the same machinist) to suit your new tonearm. That way you can have nearly whatever you want in the way of a new tonearm, so long as the P2S fits the available distance. "On-line Metals" is one company that sells what you need; they'll even cut it to your required size. Colby Lamb, in Oregon, is an audiophile/machinist who would probably be happy to do the work for you. The onus is on you to make the needed measurements. I’ve done this sort of thing at least 3-4 times, painlessly.
With all due respect to Sleepwalker, he does not seem to get the fact that the new line of SL1200 turntables (the G, GR, and GAE) are miles ahead of the original SL1200 series in terms of isolation and footing.  This I think is why he recommends the footers.  On the other hand, one might say that any turntable can benefit from thoughtful attention to isolation.  But in my opinion, your GR "needs" it much less than Sleepwalker's much older SL1200 (or SL1700, which is what I think he uses).  Sorry, sw.