Going to be honest now and you may not like it.!!

It appears to me that you don't have enough machining experience yet to justify laying out big money on machines when you don't even know what you require.
For instance the best mill or CNC machine won't make relocating your part any more accurate if you don't know how to do it.!

The fact the machine you built doesn't make the grade is purely down to poor weak design and choice of materials. The fact you can't relocate on centre is down to your low level of experience.
If you'd made fixture jigs to hold your work and indexed to a known fixed reference point then it's easy.

But your machine is so weak it will flex like jelly so this can't happen. Trying to re-locate centres without a fixture is hard at best of time on any machine and requires accurate devices to help. So no matter weak or Strong if you haven't got the abilty or the equipment then you will always struggle.

Your weak build is to blame for low part accurecy for sure but has nothing to do with reloctating and no amount of strength in the machine will helps this as it's down to you to come up with ways to fixture.

Properly built DIY machine which uses good components will easily do what you want.