If TiVo had the hypothetical CPU power to do real-time conversion from MPEG2 (over-the-air recordings) to h264 (supported by Chromecast), then the rest would be easy. You'd have a control app on your phone or something. That tells the Chromecast to load up a (whitelisted) web page which knows the internal address of your TiVo and includes the moral equivalent of <img src="your-tivo/your-video">, except doing it with HTML5 video.
Absent this, you could run a transcoding proxy server on your computer. Such things already exist in other contexts (e.g.,
PyTiVoX, which transcodes content from your Mac's hard drive and streams it *to* your TiVo). A variant on that, built for the Chromecast, should be technically feasible.
As to the TiVo Stream / TiVo Mini.... words cannot express how annoyed I am at TiVo. My TiVo Premiere has a 100Mb Ethernet on it, and reliably delivers 30Mb when I'm extracting videos. That suggests that they should be able to send at least one HD stream (19Mb) to an external device. Of course, I'm sure it's got inadequate CPU for doing the transcoding, thus the need for the $130 TiVo Stream. Or, for $100 the TiVo Mini would give me the multi-room viewing that I really want, but it only works with the newer TiVo Premier 4 box.
After some deliberation, I think my thinking is to stick with what I've got until something goes belly up. If my TiVo died tomorrow, I'd buy a new one and I'd get the TiVo Mini to go with it. If my GoogleTV died tomorrow, I'd either get another one or see if I could make a Chromecast dongle do the job.
Here's a dream: maybe someday, if/when my circa 2009 receiver dies, there will be a new receiver on the market that has GoogleTV built in. GoogleTV boxes already do some amount of HDMI switching, so why not evolve them into full-blown proper receivers? At that point, they'd have both built-in support for all the GoogleTV goodness, and would be far more seamless with external contraptions like the Chromecast dongle.