Hmmmm, I’m a little worried. The detent in the gearcase controls clutch dog positioning, there is no detent up top on the shift handle or bellcrank. So, what I’m hearing you say is the gearcase is not in neutral when the shift rod is centered into detent inside the gearcase. Loosening the locknuts slightly should not affect neutral positioning, and might just be adding slop to the linkage, which you don’t want. I’m assuming you are not concerning yourself with the visual positioning of the shift handle, it is really not important if the shift handle is perfectly vertical when in neutral. I suppose it is possible that something is binding which keeps the shift rod from centering in gearcase detent without "a little help".
Are you sure the shift rod cradle/linkage is properly installed?
Did you notice if this condition existed before you dismantled the gearcase? If this condition did not exist before disassembly, I would be concerned and would consider pulling it apart again.
Sorry, hope I am wrong. Don

Rob-
Tightening the locknuts more on top of the shift rod would only move the shift lever/handle in one direction or the other. There is no detent on the shift handle lever itself that would hold the shift rod slightly in/out of gear. The detent is in the gearcase. Again, if something is binding in the shift lever/bellcrank, that may cause the problem you are describing. Did you replace the shift rod bushing/oring? If so, I am assuming you removed the shift rod bushing in the gearcase. It may be possible that the shift rod is binding in the shift rod/bushing which could cause the symptom you are experiencing as well.
You mention that this problem did NOT exist before you dismantled the gearcase. You may not have gotten the clutch dog cradle and fork improperly positioned. Did you get both of the forward reverse gear thrust washers back in place? These washers tend to stick in place due to the oil film present between the gear and washer, they can fall out during parts cleaning though. If one or both of these washers were missing, the clutch dog positioning would be off and might cause the problem you are having as well.
Unfortunately, one thing is for sure, running the engine with the gearcase improperly assembled will create more damage, especially to the clutch dog and gear lugs.

Well, you may have distorted the ID on the bushing causing the shift rod to bind. I’m not sure I understand just how you removed the bushing, there is a special tool made for removal/installation of that bushing, Frank Robb may still have some to sell. Where do you live? Perhaps there is a member in your area who can lend you the tool. It will be tough to judge if the bushing is binding while the gearcase is assembled because it requires considerable effort to overcome the internal detent. Does it seem hard to rock the shift handle back/forth slightly? Go ahead and retighten those shift rod locknuts properly and try rocking the shift handle/lever. Driving the shift rod bushing in too far may have caused the oring to swell which may cause binding as well.
The other issue which may be hard to judge is whether or not the clutch dog fork linkage is correctly positioned into the cradle/collar that rides on the clutch dog. If you decide to disassemble the gearcase again, I would flip it over before removing the shift rod pivot screw and skeg. With the gearcase inverted, remove the pivot screw and the skeg screws. Now, gently tap the skeg off with a soft mallet so the positioning of the fork/cradle won’t be disturbed, it should be fairly clear if the metal fork prongs are properly positioned into the ears of the aluminum clutch dog collar. Another problem may be that the metal fork linkage got distorted from improperly assembly, or perhaps trying to force shift when the clutch dog/gear lugs weren’t lined up properly.