You shouldn't be maneuvering around parked cars. If you are riding correctly, 3rd and 4th are a dream to ride on because people have plenty of lanes to go around you. Although it would still be intimidating to some that they are going so fast in some areas.
I don't think any bike lanes are needed downtown. If all the streets are 25 mph and people ride their bikes correctly, then there is no problem.
Where bike lanes are needed in Columbus is further out from downtown where road conditions can be bad and there are a ton more cars moving a lot faster. Plus, further out from downtown the cars aren't expecting to be integrated with bikes. I used to ride in to downtown from Reynoldsburg and being on Livingston, Main, or Broad out that way were all hell until I got pretty close to downtown.