This is an update for people who find this thread in the future.

PDL-Fit-Levmar has been updated and is now indexed on metacpan.

It also works best of the modules I tried, converging on a solution without being sensitive to starting conditions.

My previous issues were due to my own syntax errors. The main thing is that the code examples use the form x = f(t), not y = f(x) which I was assuming when I was testing, and hence my fits were using reversed axes. Such are the consequences of not reading the manual closely enough...