MODOC
I have some good friends of mine that shoot cowboy action, and they are very good. We will race sometimes on the range starting with empty shotguns to see who can get 8 rounds off faster. I will win most of the time at around 7 to 7 and a half seconds, but my friend is doing it in right around 8 to 8 and a quarter seconds. So by that standard you would be alright, but the bigger problem you are going to run into is carying enough shotgun shells for a 15 to 20 round shotgun stage. Also I don't think the lever gun will hold up very long in major matches. If your cowboy guns are anything like my friends you won't want to tear them up in a major match.
I would however shoot a local match in a hart beat with the shotguns you are running. I can't speak for all local matches, but most local matches in my neck of the woods usually shoot about 50 round or less for the whole day. I would just hate to see you spend a lot of money to get into a big match, and break your shotguns because part sometimes are really hard to find for cowboy guns.
As for building a shotgun just for the sport you can just a easily pick up a used shotgun ( I like Benelli M2 fields) put a 8 to 9 round tube extension on it, and when you are not three gunning you can still us the shotgun for bird hunting or something. I like to bring my shotgun out when my daughters boy friend comes over.
I hope this helps.