Its a long time since I did the Arriel course but I do recall the following:
The 30 - 45 second rundown is an issue. Any LONGER than that at idle is a problem. Longer is NOT better. In this cooldown period the rear bearing temperature will reduce but after that period it is anyones guess. There is a graph around somewhere in the training notes that shows what happens, the temperature invariably goes back up.
Either prior to shutdown or running at idle on the ground, the problem is poor scavenge of oil from the rear bearing area and also oil that is prone to carbon formation. Mobil Jet 2 is not a good oil in this respect in this engine. Change to a better oil. 254 appears to work OK. Exxon (now BP) 2380 always seemed to be a good oil in this engine. Avoid "ground idle" operation. If you have been idling, run up to flight again before shutting down or even shutdown from flight so long as the aircraft has been in flat pitch for the prescribed period. This will help scavenge the rear bearing area. In some installations there is no "ground idle" for this engine.
Another problem is pilots transitioning to the Arriel from Allisons. The procedure is nearly the complete opposite and it is not unusual to find people doing a 2 minute rundown!
As to whether FSII has any benefits regarding the oil system coking, put me in the skeptics line.