Wayne you can pick up a perfectly adequate rotary for a very modest figure. It'll be a machine that you find more and more uses for - certainly not one of those crazy purchases you make that spends most of its life in the back of the shed!
Kitted out with drive board, bonnets, scrubbing pads and brush attachments it really is THE most versatile tool in anyone's armoury.
No I wouldn't touch low profile tiles with HWE, especially portable system, without a rotary on standby. I used to find every now and again with a porty, sometimes the "black death" is so bad you have to sack off the extraction and just bonnet the damn thing. Therefore I'd start off on a quite small bit first...vac very well, apply a pre-spray that you can just bonnet like a microsplitter, get the HWE on it and see how it goes. Hopefully should be OK to extract, airmovers on it then follow up with light spray of MS or fusion clean and bonnet after it's mostly dry.