If your HSS flycutter bits aren't cutting it, you may want to look for better hss toolbits.
Are you buying some specifically sold as "fly cutter" bits? Because that's a bit of a flag for me. You should be buying good quality, USA made lathe tool bits, and sharpening them yourself. If you do, I bet you'll have no problems.
I'm a big fan of using abrasives also, but most makers aren't getting acceptable quality nail-nicks, in my opinion, from them. I expect to see razor sharp corners in my nail nicks with good definition and no perceptible "abrasive" marks in it. I use abrasives because I prefer to cut my nail nicks typically, last, since it gives me more latitude to set it where I want, and adjust the attitude and general flow of the blade, clip, etc. However, fly cutter and punched nicks, look the best as a baseline. It's very tricky to get great results with abrasives.
If you're using import HSS, that's your problem. If not, what specific HSS are you using? Are you grinding your cutters, and hand burnishing/relieving the edge? Is the tip getting burned off or knocked off?