If the mower speed varies without the engine speed varying, there has to be one of three things:
1. Belt slip.
2. Cycling of the variable ratio belt drive, perhaps due to a loose part in the speed selection linkage.
3. Slippage in the final drive unit, after the belt drive. The first stage of the final drive unit is the forward and reverse selection by choosing one of two bevel gears and selecting it with a dog clutch. The last stage of the final drive is by spur gears. I haven't yet figured out a way for it to slip (except terminally, if one of the gears broke or failed to engage).
Have you had a close look at the illustrated parts list? You can download it here:
http://lawnandgarden.manualsonline.com/manuals/mfg/mtd/688_1.html?idRes=11462237Right at the moment I'm inclined to suspect Problem 1, rather than 2 or 3. Although you have just replaced the belts, if one or more of the pulleys are worn, belt slip is a plausible explanation. You may be able to check for belt slip by stopping the engine while speed cycling is occurring, then immediately checking for one or more hot pulleys. Cyclical slipping is quite possible, since the belt will heat up when slipping and eventually become sticky. When it stops slipping due to stickiness, it will cool off and slip some more. With a slipping-belt clutch system, which you have, wear to the belt pulleys happens quite quickly. Hence your problem could be due to the wheel-drive belt bottoming in a worn pulley, which reduces the amount of torque that can be transmitted. Careful inspection of the bottom of the belt, and the bottom of the pulleys, will usually show whether bottoming is occurring.
Do not be surprised that it only happens in forward drive: I doubt you run it long and hard enough in reverse for the belt to heat up.
While the dog clutch for forward and reverse could "slip" in and out of mesh, it would be accompanied by loud bangs and almost certain breakage of gears, and when it was out of mesh, there would be no drive at all, so this just does not match the symptoms you have described.