Hi Matt
Yes you can do all this, but it takes a little bit of effort to get setup correctly so it might be a good idea to involve your reseller. Making an option to switch between databases involves creating a registry export file that switches all the paths and database connection details for Recorder for each database. Note that not only must this registry file switch the database server, it should also point the machine to a different set of paths at least for the mapping folders.
If you do this then you can use a *.bat file to first run the registry import file then start Recorder, so you replace your shortcut to Recorder with 2 batch files, one for each database.
If you are going to have 2 different versions of Recorder then I must say I have not tried this, and I have a suspicion that when you switch between the versions you might need to be logged in with local machine administrator rights so that Recorder can be registered properly.

Have you considered using the user survey restriction facilities that were introduced in v6.14? If the data for each organisation is in discreet surveys, users from each can be restricted to seeing and using just their surveys. The piece on the opening page of the help says: ‘A user's access to data in the system can now be restricted to specified surveys - see User Configuration. Note that this applies to reports they produce as well as the surveys they can see but not to exports done using export filters. XML reports and batch updates will only be restricted to specified surveys if they have been written to do so. This change required a new table in the database: User_Survey_Restriction.’ The XML reports and batch updates supplied with Recorder 6 were modified for this in v6.14 but if you write your own you will need to accommodate this requirement.