Our main point of contention is that they are claiming that the right to be the sole source of "Python" software, servers, and services. We have reached out to them to try to reach some accommodation (they can be "Python backup services," for example) but they are not willing to take us seriously.
It still isn't clear to me whether your purpose here is inclusive (you don't want to lose the right to use "Python" as a trademark) or exclusive (you don't want this company to be able to use "Python" for its server products). At first I thought the former, but a close reading of your post suggests it may be the latter. Please clarify.
If your purpose is exclusive, then I can't support you. There is an open source Common Lisp implementation, originally developed at CMU in the mid-1980s, whose compiler is called Python. It is still in use. I think a compiler and a language are close enough that you have no exclusive right to the name.
