The re-built cartridge will likely sound a bit different, but certainly as good or better than anything you can pick up for $600 new.
A retipped HOMC is still a HOMC.
High Output Moving Coil cartridges are inferior by default compared to LOMC (Low Output), but the problem is the OP's phono stage without MC input.
What is really better with MM ONLY phono stage is MM or MI cartridge.
@birdfan For under $600 there are many great MM or MI, mid compliance are ok for your arm. Instead of some hybrid you can get from retipper, i would recommend to look for a completely different MM cartridge, this is all you need for your phono stage (not a HOMC). Something like this.