"The trouble is, how can I check to see it it works PRIOR to changing my name servers?"
""If you have another domain name free then you could set it up with that and change it later, or set up a subdomain on your DNS server (such as test.fff.com) - install the new MU on that and then change it later. "
That's bad advice, IMHO.
Short and simple:
Edit your hosts file. (google it, if need be)
If you're moving, but want to test first, or whatever, simply add this to your hosts file:
192.168.1.1 mydomain.tld
Replace the ip above with the ip of the new server, and the domain with your own.
If you're running subdomains, and want to test a few of those, add them as a space separated line after the main domain above:
192.168.1.1 mydomain.tld test.mydomain.tld john.mydomain.tld fred.mydomain.tld
You may have to restart your browser/computer, but you'll end up just fine.
If you need to visit the real domain, and not the test, simple comment out that line with a #.
MUCH easier, and no fooling around with this, that, or the other. Like having to edit the database to change domains, etc.