Tinker -- thanks for the informative response. Things like what types of leather stretch more/less than others is why I'm not trying to tackle this on my own. I just don't know enough. That, and I lack tools. While I'm a maker by nature, mama's tolerance for new tool purchases is pretty low. Also, it looks like I left out a critical piece of info, which is size of the chair. The measurement from outside edge of pipes (including current PU) is 18.75 inches. If you took off the seat sling and laid it flat, it would be right at 36 inches long (maybe a smidgen more). You'd probably need +3 inches on both sides to wrap the side bars though, so we're up near 24 in wide by 36 in long. That would be tight on the wrap though, so a couple more inches left to right would be better.
As for shipping, I use an APO, so the cost would be the same to ship to/from New York. If I was only sending the seating and arms, that shouldn't cost too much. If I was sending the other metal components, it would up the price a little, but probably not prohibitively so. If you want to throw a quote my way, don't let shipping costs stop you.