Just looking at the parts diagram, I would try putting some grease on the drive block bell splines and agitator. Sounds like the weight of the wet clothes might be putting extra torque on agitator causing enough movement in the splines or agitator to bell connection to create the noise. Just a thought...
Turn breaker off. Remove toekick. Use screwdriver to turn motor. Pump seal sometimes sticks to shaft keeping motor from starting. If motor turns free still will not start, it is probably the motor capacitor. GE doesn't sell it separate from the motor but have found the fan motor capacitor in a GE over the range microwave will work.
I would remove the drum for two reasons. Makes it easier to access and you can vaccum out the lint buildup. To remove the drum, reach in and take tension of the belt and slip it off the motor pulley. Slide the belt to the rear of the drum and use it to help lift the drum out of the rear support bearing. After removing the drum vaccum out the lint and blow lint out of the motor. Use a pair of channel locks or vice grips on the motor pulley to hold shaft while you unscrew the nut on blower wheel. Sorry, can't remember if it is right or left hand thread. I usually replace the rear support bearing whenever I get this far into one. Check belt and front felts or glides for excessive wear. Saves another trip into it later.
No need to remove dryer. Kill the power. Remove the front panel of the washer. Remove water level tube belt, and motor. Remove agitator. Remove screws from water inlet and move aside so tub will clear. Remove tub cap. Get two metal electrical boxes and remove the tabs for the cover screws. Remove the three small springs by gently straightening the tines that hook into base. Three heavy springs may be color coded, so make note of their location and setting in their base holders. Springs can be easily removed by moving tub to stretch spring and jam electrical box into spring to keep it opened up for easy removal and replacement. Once springs are removed, tub can be removed from the cabinet. Remove old tub seal. Remove three bolts holding plastic tub to base. Remove two screws holding tub bearing in place and remove tub. Transmission has two bolts holding it in the base. I always replace tub bearing and seals. Don't like to have to tear into it twice.
Have had the same issue. Usually found vent issue or customer cut unit off before it went through the cool down period (no heat during last 5 to 10 minutes of the cycle). Sometimes the cycling thermostat (high limit) is bad.
Replaced console on same dryer twice in less than six months. That's when I decided I was a little smarter than the GE engineers and designers. Fabricated a bracket to hold switch in place. Only modification since original design was to add shrink wrap to prevent shorting out if it made contact with one of the terminals. I guarantee it as long as the customer owns the dryer. Don't guarantee the POS GE rotary switch. Not had one fail yet.