My Snapper rear engine rider has begun making a metal grinding noise when the gear shift lever is shifted to reverse, clutch engaged or not. Also harder to shift to reverse. No noise in fwd speeds.

this manual transmission?
seems. so
the tip of shift levers love to get worn and not allowing the shift rail forks to hit 3rd gear.
a pure simple mechanical failure and is shifter tip end parts bad, some are even made of plastic.
or
3rd gear synchro- ring is super worn out and the main clutch drags. (seen it and fixed them)
if clutch has master cylinder is the fluid always at top line or drops in time every weak.

I'm a little confused on your description of the noise. If I understand you correctly It is making the noise when it shifts smoothly into gear but at the same time it makes a grinding noise ? It possibly can be synchronizers if the grooves on the inside of the synchronizers are worn bad enough to where the gear isn't slowing down enough causing a grind as the clutching teeth on the gear mesh with the synchrode and the shift collar.
If it is making noise in all gears except 4th you may have countershaft brgs failing. The power flow in 4th gear goes directly through the mainshaft and has a 1 to 1 ratio. All other gears the powerflow goes through the countershaft causing a load on the countershaft so if you have bearings failing in the countershaft you will hear noise in all gears but 4th.
i hope I understood you correctly .

Could be the clutch.
Reverse and first do not have gears that line up like the others do. So if the clutch is not disengaging all the way, they will grind.

Reverse is not "synchronized" forward gears are, so it does make some noise, try shifting to 2nd before engaging reverse to slow gear rotation and limit gear clash or grind.

No one can tell you what it is.This is the operating characteristic of your transmission and customer do object to the noise or clunk and dealer discourage the repair. This is TSB 03-07-29-004G. Let me give you a partial copy. INFORMATION
Bulletin No.: 03-07-29-004G
Date: December 15, 2010
Subject: Manual Transmission Operating Characteristics
Cold Operation
Manual transmission operation will be affected by temperature because the transmission fluid will be thicker when cold. The thicker fluid will increase the amount of force needed to shift the transmission when cold. The likelihood of gear clash will also increase due to the greater time needed for the synchronizer assembly to perform its function. Therefore when the transmission is cold, or before it has reached operating temperature, quick, hard shifts should be avoided to prevent damage to the transmission.
Backlash
Backlash noise is created when changing engine or driveline loading. This can occur when accelerating from a stop, coming to a stop, or applying and releasing the throttle (loading and unloading the driveline). This will vary based on vehicle type, build variations, driver input, vehicle loading, etc. and is created from the necessary clearance between all of the mating gears in the transmission, axle(s) and transfer case (if equipped).
Shift Effort
Shift effort will vary among different style transmissions and synchronizer designs. Usually the more heavy duty the transmission, the higher the shift effort because of the increased mass of the components. Shift effort can also be higher in cold weather because the fluid will be thicker. Medium duty transmissions will not shift as quickly as a Corvette transmission. To reduce shift effort, do not attempt to rush the shift - allow the synchronizers to work as designed. Shifting harder will only increase the chance of rushing past the synchronizer leading to grinding while shifting.
Non-Synchronized Gears
Some light duty truck transmissions in 1st gear (creeper-gear) and reverse gears in various transmissions, along with all gears in some medium duty transmissions, may be non-synchronized. This means there is not a mechanism to match input and output shaft speeds to allow for a smooth shift. This function is left up to the driver. This can be noticed if a shift into 1st or reverse is attempted while the vehicle is rolling or before the input shaft stops rotating leading to a gear grind. The grinding can be reduced by coming to a complete stop and pausing for a moment before shifting into the 1st or reverse gear. Some slight grinding can be expected. In medium duty non-synchronized transmissions, the driver must match input shaft (engine) speed to output shaft (driveshaft) speed with every shift. This can be accomplished by double clutching, or by using other methods. If the driver is not able to perform this function properly, there will be gear grinding with each improperly completed shift. Driver training may be required to correct this condition. Clutch brakes are used in medium duty non-synchronized transmissions to allow a shift into gear at a stop. The clutch brake is used to stop the input shaft from spinning, allowing a shift into gear at a stop without grinding. The clutch brake is activated by pressing the clutch pedal all the way to the floor. When the clutch brake is used, it is possible to have a blocked shift with the vehicle stationary. If this occurs, engage the clutch slightly to rotate the input gear to allow the shift. The clutch brake is intended to only be used while at a stop. Care must be taken to not activate the clutch brake while shifting between gears. This could lead to excessive grinding or a blocked or missed shift.

That sounds more like the synchro gears are out of whack rather than the clutch being the issue. If the clutch was the issue you would hear the noise whenever the clutch was engaged not just when the tranny is shifted to reverse.

It is possible that the first gear shift fork in the transmission is bent causing the 'dog-clutch' between two gears to just barely mesh. With engine off, push the shift into first and clutch lever released. Rock the bike back and forth to see if the gearing seems to be jumping in and out. There may be a problem with the shift lever shaft mechanism not allowing a complete shift into first gear. Hope this helps!

Often the transmission will clunk when first starting up and shifting into 1st. gear. To help alleviate this, hold the clutch lever in for thirty seconds or so before making that first shift into gear. This should make shifting into first much quieter.
This situation occurs on most of the FJRs, even when new.

internal slave cylinders are known to leak , unfortunate it is behind clutch assembly , i would change both , clutch master and slave cylinder

Ok, Clutch engagement point should be midway or just before midway in relation to total travel.(pretty much the same in any clutch vehicle) assuming that if put in lets say 1st gear, with clutch in,then engine started, when clutch is released, car does not move but there are no unusual noises (grinding from inside trans.) If this is the case, I'd first check linkage for adjustment. If OK, remove the trans and look inside for broken gears, excessive metal debris etc.If shift rails are internal it could be that shift forks are sliding on rails and failing to engage synchros.