I'm sure this is common knowledge, but setup and a sharp resaw blade are essential. Especially when you're asking a lot out of a smaller saw.

I have the Laguna 14/12 and really like it. Its a 110V, 1 3/4hp saw that claims 13" resaw capacity. I would bet that with a great, very sharp blade you COULD do what you're asking, but it'll take a lot of patience. I've resawed plenty of ~6" stuff, but 13" would really be pushing it, even if they claim the capability. YMMV.

We have the Laguna 14BX (220V, 2 1/2hp) at a shared shop I go to and I like that one a lot...seems like a good balance of capability and value. I've resawn wider stuff on that, and it works fine as long as its setup well and you've got a new, appropriate resaw blade.

But resawing 12" stock is going to be frustrating with all but the biggest saws I think. I think the most realistic idea is the used 3hp with a VFD.