Why are you running out of space?
It may be as simple as deleting backups.
This (server running out of space) is one of your "pressing?" needs to move forward, but will it save you time if this issue is fixed. Certainly upgrading your server is going to take an investment of time and money.
Cloud may simplify some time demands, but will still take some investment of time with transition. Perhaps short term getting IT help may allow you breathing room to determine the best long term solution.
Where is your time being used up, and how can you modify the overall system to improve it. Integrating billing may help, but many people here that do double entry billing state it is not a big time drain. If you change billing programs it will take time to learn a new system. If you outsource to a company it will possibly cost more money.
AC has a PM partner that won't probably be in place until the summer, although apparently you can work with them now expecting better integration in the future.
I would currently vote for getting IT help to get the server stable (more space) and consider short term investment in upgrading Medisoft (a program you know.) While all this is going on you can look for a longer term solution. If you have more than one location as a result of the integration of the other physician, cloud may make more sense.