You’re right that your time/salaried hours are better spent doing something other than researching the interaction between suspected vinyl, metal, and adhesives… those salaried hours alone would probably equal the cost of hiring a professional conservator to do the job right. Not including the cost of a Master’s degree in conservation though 😉
Now- as a conservator:
-First of all- I’m glad you brought it inside!
-Second- My lofty recommendation: contact a museum with a legitimate conservator in your area to (Denver Museum of Art does) to recommend an ethically practicing conservator in the area to come out and give you an estimate for work, then use the number as a fundraising goal at your next event, crowd sourcing website, whatever. You could even prioritize a few “significant” objects clearly deteriorating and raise funds for the group of them. (Like buying in bulk, grouping objects will sometimes cut down on some of overhead costs from the conservator).
-Third- Like asking a curator to write a book on a historical site for free without ever seeing the site… a recommendation on a treatment from a forum will never be right- and might cause you more harm than good / waste your time / get you a bad review with the curator in the sky.
In conclusion– If I were you, I’d get a collection of items together, be prepared to pay for at least a quote, and ask the visiting conservator to mechanically stabilize the sign for storage in the meantime, while you raise the funds to get the object(s) treated by them, based on their quote.
OR- Store it flat right in your exhibit space or board room with a sign above it asking for a donation for the cost of conservation. We all like to hide deterioration, but if the public or board never sees it, they’ll never think it is important.
And if you must, must, must do something with it; (please don’t glue it) Maybe try some twill tape or plumber’s Teflon tape (neither are actually tape, they’re like inert string) and tie it around stable areas of the sign to “mechanically” hold the letters in place in the meantime. Or a Mylar sleeve maybe…
Hope this helps; Do message me if you need assistance contacting a conservator in your area.