We've used the post submit hook in Freeform to write our own extension that submits the data to SalesForce. In this case, we use cURL to simulate a post to SalesForce's Web2Lead form rather than work with the API.
If you start in that context - An extension using the post submit hook - You can write any number of functions in there. You could submit to 1, 2, 5, 10 different services with the data that was just posted.
Updated: Another option, if you don't want to go the Extension route:
You can enable PHP in a template and set that template to be the Redirect URL of your Freeform form. Write out all the PHP that integrates with those CRMs in that template. There should be a way to get the Insert ID of the new Freeform entry onto the redirect URL. Within that PHP template, you can redirect the user to any other page on the site you wish.
Either way, it's a file with the PHP that does the behind the scenes POSTs to those sites. The extension is the right way to do it.