One option is to have the camera modified to take alkaline cells. If you look around on the net, there are also instructions on making adapters for alkaline cells and it is possible to purchase such adapters for around $30 each.
When I had an EF, I just used the Weincell zinc-air cells and kept spares on hand to replace them. It's not that they are defective in some way, but it's in the nature of a zinc-air cell to oxidize with exposure to air, so they don't last as long as other batteries. They come with a plastic cover that is removed to enable their use, and I've heard of people putting this cover back on the battery between uses to extend battery life, but I never bothered. The cheapest source I found for them was B&H.
I highly recommend the New F-1. The focusing screens are brighter than the old ones, the mirror damping is much better, and for me spot metering is a major attraction. I'd save up for one.