You're talking to someone who has studied the issue in depth. I'm not just going from an uneducated assumption.
I honestly think that a "market for force" would quickly result in something akin to feudalism at best.
Can you explain the mechanism whereby different groups weilding force would just agree to disagree and co-exist?
What would happen in practice would be that some groups are defeated, and the others pledge fealty in a kind of feudalistic system which just ends in a dictatorship.
Of course, it would be likely that some particular group (which might even win) would represent some specific ideology, and just turn back into a regular government (such as a constitutional republic).
I'd definitely be supporting the "competing government" in favor of establishing a constitutional republic.
The only way to institute such a system is to have an institution that holds a self-enforced monopoly on retaliatory force, which is the government.
Under any form of anarchism, the gang that is most successful at weilding force gains control. "Market anarchism" is an oxymoron, because markets (freedom) and force are opposites. Likewise, "anarcho-capitalism" is an oxymoron.