The bike shop was not very helpful but the project you are proposing (or a practical application of it) is going to be fairly expensive in parts and labor and perhaps you have an unrealistic view of what it will cost if they or any shop does the conversion.

I agree that keeping or replacing the rear derailleur is necessary if you want more than a single speed and that the cables and housing are a likely cause of your shifting problems.

Is there a bike Co-op in your area? These are a great resource for inexpensive parts and expert but low cost help.