Selecting Plug Accuracy Equipment
Bait Casting Reels:
When choosing the reel, you want to make sure that your thumb can rest simultaneously on the line/spool rim and on some other part of the reel (some thumb bar). That way the thumb can contribute in holding the rod AND it can apply a flexible breaking force (by bending mostly the last joint in the thumb).
Reels for 5/8s: Most casters who have cast 5/8 oz a lot and successfully will recommend old reels with direct drive: Langley (Plugcast?), Shakespeare 1973 D (Ok, but line gets into the reel a bit too easily), and Meeks. Now the Shimano TE 200 DC and other waffle spool reels offer promise.
Henry Mittel on lines:
1/4 & 3/8 oz.: For many years, I've cast with golden 4 lb Stren. Eventually, I switched to a slightly thinner but stronger line that's more or less clear. The thinnest diameter and least memory make it easier to reach the long target at 80'. Easier means more control.
5/8 oz.: Cabelas' Ripcord Si 14 lb. It takes a couple of casts until the extra silicone has rubbed off - instead of a couple of months some of the braided lines needed to be broken in.
Pistol Grip Handles:
The shape of the cork in a straight gripped Champion Featherweight should allow you to hold it (with the thumb on the reel) comfortably.
If the reel goes too far into the handle, there is no additional support for your thumb and you are likely to brake too hard when you don't want it. That's not a good situation. The only thing I can imagine that might help is to sand down the diameter of the handle cork so that your thumb gets closer to the thumb bar.
If the thumb bar on the reel is a bit too high you might be able to build up the handle with tape (first sports tape, then tourn-a-grip).