How can you win against multi-sport organizations?

I am currently involved a softball program that was just started in the last few years. Several of the local youth sports organizations came on board with us,sending girls that use to play for them in the past to our groups. We pride ourselves on being an organization offering only girls softball, with both rec and travel teams. Some of the agencies in the community have refused to join us. They are still attempting to run their own rec programs. However, they can't generate numbers to run a league and are running around looking for someone to play. These are youth groups that offer football, cheer leading, baseball and basketball besides girls softball. We are talking an average of 40 girls per group. What ends up happening is the same old, same old. Multiple organizations that have to play each other to function.
I need opinions on how to overcome this? We are trying to be better than the others, but is this enough? You'll come up with things that we are trying or talked about; I want to hear them anyway.

Am I missing something? First, what's wrong with several rec programs in the same area? Second, why do you have to have all of the softball players in the city? Third, you say your league is trying to be better than the others. How?

It seems to me that if you truly offered a superior product, then the parents of the girls from the other organizations would be moving them to your league to begin with. There would be no need to "overcome" anything.

Why do you need to overcome having several organizations in your area? What is wrong with playing other organizations? I, like YOCOACH, do not understand the problem. Why does softball NEED to be under your umbrella in your area?

Can you partner with them and create a league that includes games between organizations?

In the area where I'm at there are multiple park district and rec organizations. Each running under their own rules. They have formed a loose league of sorts and play each other. One of the groups sets the schedule based upon field availability at each of the programs involved. Nothing to "overcome" at all, just some cooperation amongst those involved. It seems to work good for them.

If you offer something that is superior in a travel program as part of your organization the interested kids will come and look at your program.

It sounds like you're wanting total control of the softball in your area. Be careful what you wish for.