XMLHttpRequest() is one function call. AJAX in this context implies a rather serious JavaScript application. I note you didn't respond to the FreeNX alternate idea. Apparently there's already MozNX, a Mozilla plugin, so that would actually take care of the display (at the cost of another plugin).
I have an even better idea, though: A bootable Linux flash drive that connects to FreeNX running on your own EC2 instance with a deniably-encrypted filesystem (TrueCrypt). You can pop it in any borrowed computer and it just acts as a terminal, with your software running on EC2 and displaying remotely on your system.
Then you can have access to your apps and data anywhere and don't have to worry about spyware or keyloggers on unknown systems (except hardware keyloggers) and only pay for the hours you actually use the system.
(If you don't trust EC2 with personal data -- since you never know who else is going to be on your same Xen host -- then use whatever co-located machine you set up yourself, also with TrueCrypt; although without the machine in your physical control at all times, it could be compromised regardless -- not to mention trojans planted in your binary distro of choice.)