Hi Jamie,
For the reverse proxy method, the search engine will perceive that the blog is on the main domain (domain y). As far as any user or Googlebot is concerned, the blog is on domain y in a subfolder – they never see domain x. If you do this, your main challenges will be:
- Making sure that domain x can't be accessed directly (otherwise, your entire blog will exist in two places). They should only be able to access the blog by visiting the correct subfolder on domain y. Domain x can be configured to only accept connections directly from domain y.
- Making sure to configure the proxy correctly. They can be tricky, and may take up some of your team's time.
- Making sure everything remains fast. Although Googlebot has nothing against proxies, if the inclusion of the proxy introduces a big delay to the page load time, that's going to have a negative impact.