I would not have started the upgrade on an old version like that without a full offline backup of the files and the database so that it would be possible to restore it exactly as it was if something went wrong.
"I tried to perform an upgrade from 220.127.116.11 directly to 18.104.22.168 but that process failed."
Should have stopped there and asked for help and described in detail what you mean by that process failed.
"So I started to do it incrementally"
bad idea, just making it harder, upgrading to a version other than the latest is just as difficult as upgrading directly to the latest version, so just more steps, more complications, more work, and more opportunity for things to go wrong
"and finally just erased all the files at my host"
another bad idea, files uploaded by users such as images used in content are stored on disk under the /Data folder, so I guess you lost that content by deleting it without a backup, there is no way to recover that so if your content had images in it those images are lost now.
"I unzipped a new copy of the 22.214.171.124.deployment files and uploaded those to a new physical installation on my host server."
another bad idea that will break things. asp.net sites can only run in an application boundary ie an IIS site or a folder below a site configured as an IIS application.
nesting additional copies of asp.net files in other folders within that structure will definitely break things
I would delete that extra tree of files
I would only have one set of the latest deployment installation files uploaded to the root of your web site. ie the contents of the wwwroot folder in the deployment package should be uploaded into the root of your site so that the Web.config file lands in the root and dll files land in the bin folder and other files land in the correct folders.
I would watch very carefully for any ftp errors during upload and retry until all the files get uploaded. Then I would visit the /Setup/Default.aspx page
it should be possible to get the site working again since most content is in the database but as mentioned you may have missing images since you deleted the files