Since these systems come with Core Duo processors, I think they should also support some of the first gen Core 2 Duo mobile chips (I’m thinking like the T7200). Those chips support 64 bit and should be pretty cheap to come by, if you’re willing to do some surgery on the laptop.
Yes, the T60 is socketed, so I did upgrade mine to use the T7600. The X60 is soldered, though. The rare 64-bit X60 laptops do come with the T7200. There are some X60 tablets with a with a weird 64-bit CPU that's only 1.5 GHz or so.