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'98 200 Yammie SWS II runs great up to 3000-3100 RPM. Starts and idles fine. Accelerating above 3000 RPM causes it to bog down and lose RPM's for a few seconds, then slowly speeds up. Will eventually reach 4400 RPM if hold stick down long enough.

Any hints to try and fix or should I raise the white flag and surrender to the outboard shop? Any shop suggestions (I am in South Georgia)?

I had trouble like you are talking about it mine also ..I hate to say it but It might at one time or the other had a oiling promlem and u seized a pistion..
but then im not a whiz on YammiesYou need to have a compession check done .

It could be as simple as a dirty fuel filter to as bad as SD said I would check the filter first, the next time running it, try activating the choke or squeezing the primer bulb and see if that makes a dif. in the above 3000 range

I would see if your primer bulb is hard or colapsed when you get above the threshold. You might have a pinhole leak in it causing a lack of fuel when the high speed jets kick in.

WHAT TOM SAID, YOU ARE LOOSING THE VACUME ON THE FUEL LINE, BE SURE YOU HAVE THE VENT SCREWED OPEN AND CHECK THE TIES ON THE BULB, THEY WILL GET LOOSE AND YOU LOOSE THE VACUME. IF IT CONTINUES GET NEW BULB. ONE WAY TO CHECK IS TO DISCONNECT LINE FROM FUEL TANK AND IF YOU HEAR A SWOOOSH, THE VENT VALVE IS NOT OPEN, IF THE BULB STOPS BEING COMPRESSED WHEN YA DISCONNECT FROM THE TANK, AND YOU DO NOT HEAR A SWOOSH, REPLACE THE BULB, IT IS DEFECTIVE. HAD A SIMILAR EXPERIENCE WITH A SUZUKI 140 ABOUT 5 YRS AGO, REMOVED THE CONNECTOR FROM THE TANK AND REINSTALLED IT AND SHE WENT FINE FOR ABOUT 45 MIN. THEN HAD TO DO IT AGAIN, REPLACED BULB AND HAD NO MORE PORBLEM.
PA THE OLD MAN OF THE SEA

If you are near Valdosta, take it to Valdosta Outboards out by the freeway. They'll fix it good and for a decent price too.