I'll try to help you, but my english is not the best, so sorry for that in advance
If you are perfectly sure that your engine doesn't have any problems, while shifting manually with the cables disconnected, there probably is to much "play" in the complete mechanics together.
Reasons for that can be found in either the remote controll, but most of the time in worn shift & throttle cables. Don't buy new Ultraflex or Honda for that. Quicksilver (mercury) has a set of very fine & precise "platinum" cables in their assortiment which solve most of those problems forever. Please don't invest your money in them exepsive cables before you're absolutely sure that: 1. There is no play in the mechanics of your remote. 2. Your engine shifts properly without remote controll cables attached.
If you're engine appears to have problems too with the shift cable disconnected, the problem will probably be in your gearcase. Most of the time you're dealing with worn gear-cams (don't know if I translated this properly). I mean the little blocks on the gears which grab the shifting clutch when shifting. They quickly get "round edges" when shifting mechanics are not properly set. Seeing them edges with your eyes, does make you think that that's not the problem, but an experienced dealer can tell you if their worn or not in one look.
In that case your gearcase has to be opened to check. When you don't have experience with this, please see your dealer for this..
Good luck solving the problem!
Regard Wouter (NL)