Blindly converting to FI is illogical.
There are many things that can cause a rough idle.
From your post, it is not clear what this mechanic already checked and ruled out. So you need to start with the basics.
Who will be troubleshooting this going forward? If you, then check and rule out one item at a time until the problem is resolved or the problem is plainly clear. If a new shop, then clear communication is key because, to make money, the shop will be incented to rush to a conclusion and throw parts at the problem.
I am somewhat confused why the original person decided that a cracked exhaust manifold or clogged cat would cause a rough idle. A cracked exhaust manifold just makes noise, unless it couses a cylinder to go lean and burn a valve. A bad valve is easy to diagnose. Similarly, a clogged cat does not cause a rough idle - but it might make it impossible to run at highway speed. If you did not have these symptoms as well, I wonder if you got bent over.
You will need to check all the basics. For example, you might have a vacuum leak - a hose or the intake manifold, that sort of thing.
Your statement that the carb constantly needs to be cleaned must be better understood. Have you installed a quality, low-micron fuel filter before the carb? If there is dirt coming thru, that would prove it before you took the trouble to drop the tank.
At this point in the process there will be more questions than answers. Troubleshooting is a logical process of testing and ruling out. Let us know more about what you have, what you absolutely know, what you are not sure about, and who will be doing the work.