I have a hard time believing a base gasket would cause that big of a issue. My first thinking could be wrong. Does it seem like it's lacking fuel when it dies, or is it loading up? Possibly too much fuel.....Meaning floats too high or too much fuel pressure? I assume you're using a pretty decent sized electric pump.
P.S. Robin, I have to say that my thinking is in general terms. I've never worked on a late model conversion, and don't really know about the ignition requirements involved, if the problem could stem from that.