Here’s a suggestion.
If Franken resigns, his appointed replacement would only serve until November 2018, when an election would be held for his replacement.
So here’s the suggestion: let the people of Minnesota decide. Franken resigns, with the understanding that (a) he won’t be appointed for the vacancy created by his resignation, but (b) if the people of Minnesota vote him back in next November, it’s no harm, no foul.
A year on the sidelines seems to me to be a reasonable consequence for his actions. And if the people of Minnesota decide next year to extend that period, that should be their choice.