I've tried several things, in order to have TB extract the addressee from the attached file with some regular expression in an template.
However, whatever I tried TB executes the template before the file is attached.

Therefore I came with this workaround, I started TB with the /Mail parameter and set the file name as To address, TB doesn't care whether the specified address is valid or not, but it takes it and executes the template. In that template I used some regexp to correct the address.
I'm using two files to achieve this, a sendfile.cmd containing one single line:
For %%i in (c:\temp\*.txt) do "C:\Program Files\The Bat!\thebat.exe" /MailT=C:\temp\Sendfile.tpl;A="%%i";To="%%i";A="%%i";Send
And a sendfile.tpl, as template. Containing this:
-----Start of Sendfile.tpl-------------
%SetPattRegExp='C:\\Temp\\(.*?)\.txt'%-
%RegExpBlindMatch='%To'%-
%ModifyOnce(To)%-
%SetHeader(To,%SubPatt='1')%-
Hi %ABToFirstName="%ToFName",
I hope you like this.
Regards, %FromFName
------End of Sendfile.tpl--------------
Notes:
I stored the sendfile.cmd, sendfile.tpl and the files I wanted to send in the directory C:\Temp, you can change that, but in that case you need to change the path in the .cmd and the .tpl
In the regexp in the .tpl you'll notice that the backslashes in the path are doubled, that's because the backslash is a special character, so I needed to escape it. the same goes for the dot before the txt extension, so I neeed to make that literal with a backslash.
My preferred method of executing the cmd file would be to do that from some scheduler, whether that's the one from Windows, TB or some third party doesn't really matter.
I intentially didn't handle the part of moving/deleting/renaming the sent files in the sendfile.cmd. When you execute the sendfile.cmd from the Windows Scheduler while TB was closed, you'll find that the files are deleted before TB was ready to send them. So my preferred method would be to achieve this via a sent messages filter. In order to make this simple I set the subject of the sent messages to contain the full path of the attachment.
I've tested both the regexp and the cmd of the posted solution. My only alteration was that I added the Send parameter after the testing, as I didn't want to send the files myself.