A while back (mostly through some generous gift giving) I mad the switch to HSS Forstner and sawtooth bits for those tasks that call for them. I had become quite adept at touching up my HCS Forstners partially due to the fact that they need it so frequently . . . I'm not complaining, the set I bought on sale at Woodcraft over 10 years ago is still very serviceable. The move the HSS and the joys of very long term use without the cutters losing their edge was a great thing. Alas, eventually all cutters need attention or replacement.
Here's where the mental percolating started. My auger files and EZ-Lap diamond paddles and cone shaped stones had served me well on the HCS. The file slipped right past the HSS and this was the main stumbling block. The stone and diamond abrasives still did OK but, the auger file was my preferred weapon for the broad face of the Forstner bit.
My DMT diamond products have outlasted all others so I gave the Folding Flat File a try. Granted they are brand new and cut like it but, it is the shape that makes them a winner for me. They have "safe" edges like one end of the auger file. This is probably an unintentional benefit for me . The thickness of the substrate at about 1/16" is nice for tight spots as well. they are stiff enough to allow a controlled stroke but, will flex under extra force so getting a feel for them is a good idea before you take after a $50 bit.
I went with a coarse and a fine. Unless you are repairing some sort of damage to a Forstner (where'd that screw come from!?!) these two grits should handle your needs. I also gave them a shot in a pesky router profile I have partiall touched up from time to time. It was noice to get into the more challenging spots with a confidence of control. It is so easy to make things worse as opposed to better if you cannot control your abrasive DAMHIKT.
I just wanted to share in case anyone else had found themselves struggling with this. Like any sharpening task in my shop, I store up a few things to do, setup to do it and then knock it out. that is; I do not have a dedicated sharpening area but, can setup and tear down easy enough that I will do it.