What happens when VFR conditions change over a longer flight?
You wrote:

"you should not continue your flight using VFR, but you can't land"
"and the smaller airports around you are not currently staffed."

Why can't you land?   If you can't land, you should not be flying!
Why do you need an airport to be staffed to land there?
Pilots land at unstaffed airports all the time following CTAF (Common Traffic Advisory Frequency) procedures.

If weather conditions are deteriorating below VFR minimums, then landing at an airport is 100% an appropriate course of action.