I can't comment on everything you asked, but I recently bought a 1991 777DY in much the same condition as yours, so I do want to throw in my 2 cents in case it helps you come to a decision.
I think as rarity goes, I think any of the 777 variety will become more rare as time goes on. Sadly, I've noticed that these guitars just aren't as well taken care of as other types, so you might see fewer and fewer in the condition that yours is in. This is just my observation, I have no proof to back it up.
As for it being a tool, I can't imagine thinking of a 777DY as a mere tool. A Jem doesn't bring anything to special to the table other than flavor. It's all flavor, IMO! Tone-wise and playability-wise, they're really nothing special beyond your typical RG. My point is that you should really question its sentimental value to you before you sell it. Figure out why you bought it in the first place.
And finally...ever considered just not insuring it? I understand the concept of insuring something; if its a tool for your livelihood then you need to insure it. I also understand the idea of recouping a loss.
What I DON'T get is how recouping a cash amount is really going to help recoup something that is very rare or even one-of-a-kind. Like if Steve Vai insured Evo (which I'm sure he has). If it was stolen, what would he do? He can't exactly buy another Evo, can he? Offer the insurance money as a reward for its return?
Also, I cannot see anyone who regularly has to sell instruments just to pay the bills as someone who's in the position to consider insurance. Where I come from, even life insurance is something reserved for those with disposible income, not something who's in the "ends-meet" category would probably care about. Hell, I'm lucky I have it through where I work in addition to the policy my mother has on me from years ago! I'm assuming you're in the "disposible income" category.
So I'm doubting that if the unthinkable happens, your stolen Jem won't mean you all of a sudden can't pay your rent.