I would pick a TT with a Tonearm with removable headshell.
then, a second headshell, this one allows azimuth adjustment
https://www.ebay.com/itm/293416434592?hash=item4450fb7ba0:g:fWQAAOSwq4VeXaps
now you can keep your 2m red, and
try another cartridge in the new table, either the factory supplied/mounted cartridge; or
an upgrade they will mount for you; or
separate cartridge (needs mounting with all alignments and settings).
no matter what table/arm/cartridge:
you need a few inexpensive tools and alignment skills to achieve the best results and avoid problems.
you don't like to fiddle, but can you set one up initially?
then, a second headshell, this one allows azimuth adjustment
https://www.ebay.com/itm/293416434592?hash=item4450fb7ba0:g:fWQAAOSwq4VeXaps
now you can keep your 2m red, and
try another cartridge in the new table, either the factory supplied/mounted cartridge; or
an upgrade they will mount for you; or
separate cartridge (needs mounting with all alignments and settings).
no matter what table/arm/cartridge:
you need a few inexpensive tools and alignment skills to achieve the best results and avoid problems.
you don't like to fiddle, but can you set one up initially?