Where are you seeing that the address is required? Whilst I can see it mentioned on a few random website, none of the official TRS websites include this requirement (eg, here or here) - only that it needs your name on it.

The site you use to make the claim also states the same thing. Step 3 states "Tax invoices for $1,000 or more must also show your name (and only your name) as it appears in your passport."

It's been about 4 years since I last used TRS for something >A$1000, and I just checked the receipt for that purchase and it does not have my address on it, just my name. It's a legal requirement that all Tax Invoices for amounts >$1000 include the buyers identity (ie, name) - the main reason it's specifically called out in the TRS rules is that it has to be *your* name. ie, you can't claim against something that is recorded as having been bought by someone else.