So the Pioneer 600/620 are early Piston Ported design, right. Not reeds valve of the era. What is piston condition?
Okay, so I'm wondering something. Any chance you have extreme worn or cracked piston intake skirt? Could symptom be related to Intake free-porting condition. Intake stroke not sealing off sufficiently after few minutes run from metal expansion effects. Maybe behaving as weird port timing.
Or, did previous owner botch a porting job; intake too low or transfers way to high. Take a look down Intake & Exh Ports for evidence of grinding work or trashed piston skirt.
If you don't mind a flooded crankcase & drying it out.
- when skirt drops below Intake Floor (should make semi 'closed' port). Should hold a pool of gas mix on the intake port, should not immediately drain thru to crankcase. Yes, leak slowly thru piston clearance & transfer channels path. But, if not "test pooling" a moment than may suggest very poor intake stroke closing. (Builders/Porters please comment... just what I'd evaluate, DIY)
Just saying because done it... broken reed test. A tight Reed Valve motor on it's down stroke will hold "test pool" over intake boot a decent time (15-30 sec). Only freely shallow after rolling crank.
I had a similar rich restricted speed issue on twin B&S. Alot different but about the same symptoms. Only turn half RPM as dead rich, but idle fine. Finally found previous owner had installed Camshaft mistimed to Crank (off by 7 teeth). Compression was 165. Motor just couldn't breathe to make RPM where a okay Carb mixture & correct crankshaft basis Ignition Timing.