Mail.app won’t start

This is really weird. Sometime later than July this year, Mail.app would go "not responding" as soon as launched, never opening any window.

system.log shows a lot of errors, but the very first is

Sep 15 19:55:02 Adminadabs-MacBook-Pro Mail[7758]: AllSignatures.plist: Syncing with cloud — merging; local data, no cloud data not reachable, error: Error Domain=NSCocoaErrorDomain Code=260 "The file “ubiquitous_AllSignatures.plist” couldn’t be opened because there is no such file." UserInfo={NSURL=file:///Users/wgroleau/Library/Mobile%20Documents/com~apple~mail/Data/V3/MailData/Signatures/ubiquitous_AllSignatures.plist, NSFilePath=/Users/wgroleau/Library/Mobile Documents/com~apple~mail/Data/V3/MailData/Signatures/ubiquitous_AllSignatures.plist, NSUnderlyingError=0x7ffa81dd8de0 {Error Domain=NSPOSIXErrorDomain Code=2 "No such file or directory"}}

The first thing noticed in that message is a mention of "cloud" but not "iCloud." Just in case they're the same, I note that in system Prefs for iCloud, Mail is NOT checked, nor is Keychain.

Next is that some file associated with signatures is missing. That file is so deep in the file system, I couldn't have deleted it by accident. But in going through backups, I find two more oddities:

First, that though Mail quit recently, that Signatures directory is missing from ALL backups. Time Machine prefs have no exclusions.

Second, that my earliest backup is the beginning of this year, when I'm sure I have been using this drive a lot longer and it is only 39% full.

What other than Mail would delete the entire signatures directory and/or prevent its backup? If it were done by a function within Mail, I would not expect Mail to be disabled by it.

How can this be fixed with no backup available? Could I copy someone else's signatures and then edit them back to mine?

UPDATE: The admin account and a non-admin account on the machine also have no signature directory, and Mail runs fine for them. SO, I conclude that the directory was created when I created the first signature, and some other plist is telling Mail it needs to open those signatures. Where would that plist be?

ANOTHER UPDATE: I scanned the directory and found that the last file mod date in ~/Library/Mail was 3 Aug. I restored a 1 Aug from Time Machine and launched Mail. The convert to new version dialog appeared. When it "Imported 1005 of 1005 messages … Time remaining: About a minute," the beachball appeared. Still there twenty minutes later and the Dock icon is "not responding"