I have an early 80's "Harmony" strat that I have customized to a degree. I love it, but the neck is a bit narrow for me.
Would it be worth it to try and fit a wider neck? I have to take some measurements to see how much actually has to change on it. I know the string spacing on the bridge is narrower than say a Fender spec, so I may want to change that too. I may put a fixed bridge on it since I don't use the trem at all, so I will probably have to fill the cavity for the trem block, but I don't think I would do anything with the spring cavity.
I have modified neck pockets before with a measure of success, and I would like to try this.

Do you think it would work?
I've put Fender replacement strat necks on Lotus and Harmony copies before. The pocket fits just fine in most cases. Make sure you don't get one with the pre-drilled neck holes, you'll want to do that yourself.

If you want fatter, take a look at the 59' profile Strat neck. It's pretty chunky.