What you could do is create a new domain with a new host. 1and1 will throw in the domain with even a basic plan. You can upgrade later. Your out of pocket will be less than twenty bucks.

Move your content from Geocities and set up meta re-directs on the main pages: home, sitemap, about, privacy, contact, etc. and replace those pages with a simple page that tells users they are being re-directed. Give it 15-30 seconds delay before you jump. SEs will understand if you follow the next step.

Add the new domain to your WT profile as soon as it is propagated (you can access it via WWW and upload G's and Y's verify html). Create a Google sitemap as quick as you can that points to the new site's core pages (especially). You can expand on it once your domain is indexed.

It will be especially helpful if your existing site(s) are indexed and registered in WT. But no matter. As you relocate pages to their new domain, they can be added to your xml sitemap and deleted from their old location. Once they return 404, they can be successfully removed from G's index.

Be sure your navigation points from at least one (any) indexed page to any page you install anew, else it will be missed in subsequent crawls.

Be careful not to remove the core pages into which you have installed your re-directs. Eventually you will have just those pages remaining. At that point, Geocities can do what they want. You'll be up and away without skipping a beat.