I have a New F1 and it is a wonderful camera, and have been using the Canon FD system for a while. In my experience it is the best return foryour dollar, especially in terms of lenses.
However - you already have an excellent camera, and a couple very useful lenses, and the price difference between older Nikon lenses and Canon FD lenses, while it is there, is not all that big. You have a camera right now that is at least as capable (and I would say slightly more) than the New F1 - you would not be gaining any significant capability by the move. And then you have to go out and buy some lenses - no matter how good a value they are, they are still an expenditure. And you already started with one system, so you would have some redundancy or a system that is built at the expanse of another - not the most practical solution.
If I was in your position, I would get an affordable back up body for your F3 and invest in some of that excellent Nikkor glass - the only reason to buy the F1 that I can think of is if you just really want to have one. And this is coming from a Canon (New F1 among others) user.
PS - The only significant adventage I can think of in the New F1 is a) the ability to install a focusing screen wich gives you a spot metering capability and b) the super fast motor drive (8.5 fps) which I think would requie the dedicated high-speed F3 to match (if I recall correctly). Unless one of, or both of these are really big on your list, the F3 does just about everything the F1 will, and some things it won't (MLU, for example).