A slightly out-of-the-box method would be to script up a solution in AutoHotKey. I use this, and it's not perfect, but works and is free. Essentially, this script assigns a hotkey to CTRL+SHIFT+R which will copy the selected SQL in SSMS (CTRL+C), save off a datestamp SQL file, and then execute the highlighted query (F5). If you aren't used to AHK scripts, the leading semicolon is a comment.
;CTRL+SHIFT+R to run a query that is first saved off
^+r::
;Copy
Send, ^c
; Set variables
EnvGet, HomeDir, USERPROFILE
FormatTime, DateString,,yyyyMMdd
FormatTime, TimeString,,hhmmss
; Make a spot to save the clipboard
FileCreateDir %HomeDir%\Documents\sqlhist\%DateString%
FileAppend, %Clipboard%, %HomeDir%\Documents\sqlhist\%DateString%\%TimeString%.sql
; execute the query
Send, {f5}
Return
The biggest limitations are that this script won't work if you click "Execute" rather than use the keyboard shortcut, and this script won't save off the whole file - just the selected text. But, you could always modify the script to execute the query, and then select all (CTRL+A) before the copy/save.
Using a modern editor with "find in files" features will let you search your SQL history. You could even get fancy and scrape your files into a SQLite3 database to query your queries.