I'm going to take a stab here, but may come back if other ideas occur. I do think that a university funded virtual research position is unlikely unless you are a superstar in your field already. Lots of regulatory issues stand in the way.
First option. Find some funding to support yourself adequately. This might be in conjunction with someone at another university on a common project. Since this might take a while to arrange, it might be necessary to delay the sabbatical for a while until you secure the funding.
Second option. Find a collaborator who already has a fairly large grant and is doing something that interests you. I think that applied math might offer some opportunities here. If you already have a wide circle of contacts in your field of interest, start to ask around what they can suggest. Maybe send you along to someone else, even.
Sub option under #2. Perhaps you have a colleague elsewhere who is willing to "sell" your participation to their administration and make some guarantees as to the quality of your work. That is, you don't apply directly (at first), but arrange to get invited. This would require a pretty strong argument on your colleague's part, but it could, in principle, catapult their research to everyone's advantage.
Third option. Not a research university, but some research lab (governmental, commercial, non-profit...) that is very interested in what you do and needs help badly enough that they are willing to provide funding for a virtual team member. Probably rare, but not as rare as a university funded position.
As you know, the virtual doing of it isn't all that impossible nowadays, but the funding for a person who never shows up and introduces difficult tax and supervision issues is a hard sell.
