Kyle,
I have overlayed asphalt in the past. However, you really need to look at the issue that is causing the paths to be redone. If tree roots are an issue, obviously take care of the issue before adding another lift. If you have some raised areas, check out
http://www.flatpaths.com. This guy provides a service that will smooth your raised areas buying you some time before venturing into resurfacing your paths. Additionally, when you resurface, I would avoid patching areas as it is hard to get the transition from old to new smooth without doing additional grinding of the edges. In the one case where I have overlayed paths, I used a road contractor but had to call around to several before I found one that had small enough equipment(layers and trucks) to service my needs without ripping up the course in the process. We also ended up ahving to use skid steers to feed the machine in smaller areas in which we couldn't get a truck. Keep in mind that this will also cost you a lot more than what a typical road resurfacing project would go for.
As for concrete, I use traditional concrete guys. But again, you may have to call around before finding one that is willing to do areas on your course with limited access. This is also going to cost more money since often the contractor will need to rent smaller, more specialized equipment to get the mud out onto the course without tearing things up. Often though, a golf course construction company has the expertise and equipment to do this slightly cheaper than a contractor, but will require a minimum square footage before even accepting the job.
Down here, we can typically have concrete poured for $2.25/sq on new construction and closer to $3.00 for repairs including removal of old, form and pour.