Hi,
Is this a tiller model or remote control?
When you say that you adjusted the linkage, do you mean:
under the hood?
at the shifter console (remote with cables)?
or at the shift rod/shaft that sticks up out of the front of the gearcase?
Reference items 11, 30 and 12 in the link below for the shift rods and adjustment nut:
Buy OEM Parts for Honda Outboard 20HP WATER PUMP + VERTICAL SHAFT (S,L) Diagram
www.boats.net
My first thought was that the shift rod just needed a minor adjustment. That's the first thing that should be checked in a case like this. Oftentimes the jam nut holding the longer adjustment nut comes loose and the adjustment gets out of whack. Sometimes it's just that the shift rod wasn't properly adjusted in the beginning and it has just "drifted" that tiny bit more to cause this issue.
If you adjusted anything other than the shift rod, you may need to go back on that to get back to a place that a shift rod adjustment will be effective.
With the other shift components back to their former settings, the shift rod can be adjusted.
Sometimes it's best just do a "base" adjustment.
....NOTE: Anytime you shift ANY outboard that isn't running (dry shifting) rotate the prop slowly at the same time. It doesn't matter in which direction. It just needs to be slowly turning to prevent the clutch from hanging up so that you don't accidentally bend the upper or lower shift rods.....
Shift the outboard into reverse to fully expose the adjuster and jam nuts on the forward exterior portions of the cases.
Loosen the jam/locking nut while holding the long adjustment nut (item 11). You will need two 10mm open end wrenches.
Turn the long adjustment nut clockwise so that it climbs UP the upper shift rod (item 13 in the link above) and disengages the lower shift rod.
Rethread the adjustment nut onto the lower shift rod slightly then turn it so that it travels down the threads for 3/16".
That will USUALLY give a good adjustment but is considered preliminary until you test it. Tighten the jam jut keeping in mind you may need to loosen it again if necessary.
You will then need to either run the outboard in a tank or trashcan with water (I don't recommend muffs for this) to ensure that you do have a good adjustment with proper gear engagement. Try it several times at idle. Neutral to forward- pause-back to neutral-pause-neutral to reverse-pause- reverse to neutral. Once you are satisfied with the adjustment, tighten the jam nut securely. Don't "muscle" it down but do keep in mind you never want it to accidentally loosen on it's own.
I'll tell you something many boat operators don't know but should.
Outboards have "dog" clutches. Because of the way dog clutches engage, it's important that shifting only be done at idle and gear selection should be made with a swift, firm motion to keep the clutch "ears" from bouncing off of each other while rotating.
A slow, "lazy" gear engagement will often result in a chattering noise from the gear housing. That chatter is the sound of the dog clutch being slowly ruined.
Just sayin'.
If this adjustment doesn't straighten out this problem for you then the next place you will want to look might be behind the propeller. You WANT to periodically look there anyway because it's important to do so.
There is a thrust washer behind the prop and it can be a high wear item. I personally consider thrust washers as "consumable" items that often need replacing. A badly worn thrust washer is bad for the gear housing and might even set up a "prop pulse" situation during low speed, low power operation because of the excessive clearance it allows.
Bent blades, or a worn, damaged hub could also cause noises from the lower end.
Also you want to take a peek in there because things (like fishing line) tend to wrap around the shaft and that can cause damage you don't need like a leaking prop shaft seal.
Hope you figure it out.
Please let us know what you find.