I went ahead and did the above. For anybody wondering where you can find the install path in the registry:
Open up regedit, go to HKEY_LOCAL_MACHINE and navigate down to software and lastly you have a folder called Presonus. Modify the key by right-clicking on it and enter whatever location you moved Studio One to.
You should however add the option for a custom install path from the get-go Presonus. Keep in mind that a lot of users have split partitions where they reserve a smaller amount of storage for windows and the rest for user data.