Opinions on Rega Apheta 3 or 2?

Glad to hear, that third party options are great. There is a pretty good deal on a slightly used ZYX R100 and I might go with that. I also saw on the Rega website that they discourage shims and VTA adjustments don't make that much of a difference.   

Why do you want an MC cartridge? 
Owned several very expensive ZYX like Airy III and Premium 4D i ended up with MM and MI cartridges and with your tonearm/turntable it can be better. The problem with ZYX is retip, cartridge has sealed boby. My advice is to stay away from the ZYX, there are better MC if you looking for MC only. 

I'm not married to MC. I currently have a Clearaudio Virtuoso (MM) which I actually like. I'm open to any cartridge that can bring out the best in the new TT. That said, I'm also curious about MC because I have never used one.

You could find a better cartridge than Virtuoso MM, mainly because the stylus is Elliptical and cantilever is Aluminum. This combination is nothing special, also the generator of Virtuoso is Audio-Technica (OEM). However, having the best cantilever and best stylus profile together can be very costly, but well worth it in my opinion. 

So i could highly recommend you MM cartridges with Boron Pipe cantilever like SONY XL-50, great vintage MM for reasonable price, Boron Pipe cantilever is very rare option, none of the modern cartridges have this option.  A tip mounting hole made using a laser beam.

From Technics research:  "Somewhere in the high frequencies, every cartridge has an undesirable resonance point. Undesirable because there the frequency response curve climbs a sudden peak. If that peak is in the audible range, your records sound not as intended. That resonance frequency is determined by the total effective moving mass of the vibrating system - the summed masses of the diamond stylus and, most importantly, the cantilever and magnet, etc. To shift that harmful resonance frequency up into the high supersonics, the effective moving mass must be reduced to the lowest possible minimum. Also, too much effective moving mass increases the mechanical impedance, thereby negatively affecting the cartridge's tracing ability."

Another example is Grace LEVEL II BR/MR with Boron Pipe cantilever as you can see on my image, but this one have Micro Ridge stylus tip (one of the best profiles with long life up to 2000 hrs). There is a cheaper Ruby version of the stylus. Look at the Grace Level II cartridge. I love Grace, collect them, got some spares of the rarest models. 

If you like ZYX you'd better look for ZYX owner design from the past, it is interesting that Nakatsuka-San designed ADC TRX Induced Magnet cartridges for American brand ADC after ADC original owner and designer left the company. Nakatsuka-San designed TRX series, the reclacaebla stylus screwed to the cartridge body, look at Sapprire Cantilever and VITAL III diamond. Induced Magnet (or Moving Iron) cartridges are heavily promoted by SoundSmith today if you will watch his lectures. 

Stanton collector's series 100 is another gem, CS-100 with Stereohedron II stylus is amazing! Cantilever is sapphire coated (like no other model from Stanton). This cartridge is better than 981 series! Slightly cheaper alternatives: Pickering XSV30o0sp or XSV4000 with Stereohedron tip. Stanton/Pickering is another brands that i collect (all top models), the sound is so sweet. 

All mentioned cartridges are as good or even better than most of my LOMC

You have definitely talked me off ZYX cartridges. I will look into the other mentions you've laid out.