Hi Matt,
Unfortunately right now, MethodAPI doesn't provide users a functionality to check what Method Apps are installed on the account.
You can try to use MethodAPIGetScreenURLV2 call to check which Apps are installed, however the solution will be extremely unreliable. The way you will check is by looking if a screen that is used in a specific application that you need is available or not. If the screen is not available, you will get a message "Failure. There are no tablinks within the tab with the name 'Tab Link Name'", if it is, you will get a 'Success' and a URL.
This solution will not work if user is not logged in. It will not work if user deleted/moved that screen. It will not work if user created a screen with the same name.
Thank you
Victor