It is bad enough that I can't even change my account name from the original address I signed up with... (or can I?)
The rest of your questions have been answered, so here's the answer for this one:
To change the account name / address, simply change it in your mining configuration, i.e. the "username" that you are using to mine. Say you are mining with bfgminer; if you are mining to address ABCDG, i.e. your bfgminer commandline looks something like "bfgminer blahblah -O ABCDG", and you want to mine instead to address HIJKL, simply change it to "bfgminer blahblah -O HIJKL". Simple as that. ABCDG will still receive whatever payments were owed to it (after some delay, depending on how much BTC is owed and whether it has hit its threshold), but all new shares will be credited and paid out to HIJKL. You can change your mining address at any time.
With Eligius, you never "sign up" with any username. You simply submit shares under whatever address you want to be paid out to. You could theoretically change your mining address every day, or every hour. The pool doesn't keep track, nor does it care. You will still have to sign a new message with the new address if you want to set NMC payouts or the payout threshold.
But any bitcoins you have on your old account wallet address, will remain there or be merged back into the pool's resources if they are low enough. Neither you or support can transfer any remaining balance from the old account wallet address to the new one. This is per the Eligius FAQ.