Sorry, I can't help you with the "bunch of errors" you get. I don't have a Mac, so I can't test LabChirp on Mac myself, but I know of a few people who have got it working through Mono. After installing Mono, all you should have to do is open a terminal and type mono LabChirp.exe (or the full path to LabChirp). For instance, on Linux I can open a terminal and type mono "/home/labbed/Downloads/LabChirp/LabChirp.exe" and it works. For convenience, you could create a terminal script for future use.
LabChirp is not a Mono application, or a Cocoa# application. It is a .NET application. So I don't think I can use macpack.
However, I've heard that .NET CORE has a lot better native compatibility with Mac (and Linux), so I might give that a try for a future release if it isn't too much of a hassle to migrate.