I know you asked this question quite awhile ago... years ago I had this need and didn't find anything free & available at the time, so I created a script to do essentially what you are seeking in Autohotkey. It can be found here:
It's quite flexible and can be modified to do things other than just putty (my example includes RDP). Have noted your profile and can see you're proficient with code, so you might appreciate something that you can extend and modify, even automate.
At my workplace our list of servers can be exported from the config mgmt database in a CSV format, so I can actually auto-populate the config file for this script on whatever interval necessary.