@OP, I've been delayed in posting on this topic due to ID verification issues which, self evidently, are now sorted.
In answer to your opening post, it makes no economic sense to upgrade an LP 12 from the early eighties on the budget you are planning. To get that LP 12 to an acceptable standard, you'll end up replacing everything except the plinth and top plate and, possibly the motor.
The reason why there have been so many upgrades to the LP12 over the year is that the standard deck doesn't sound very good and buy the time you eradicate it's various problems you end up with a very expensive turntable that is up against serious competition.
At your price point, the Technics SL1200 G is a good option. In terms of the Clearaudio options, they are worth considering, although personally, I'd prefer to start with an Innovation Basic which, with arm, would be outside your budget. I think at your price point, a Rega Planar 8 is certainly worth a listen.
If you want to stick with a suspended subchassis turntable, the Michell Gyro SE is a good alternative.