Peter,
When I was shooting PPC for our department pistol team back in the late 1970's, I shot about 1,500 rounds of 148 grain HBWC bullets a week in practice, and then 360 per weekend in matches. We experimented with bevel base bullets, but could never get the level of accuracy at 25 and 50 yards with them that we could get with HBWC bullets. I used to have a target from my K-38, fired from a Ransom Rest, with 148 grain HBWC's, that was 10 rounds in 1 7/8" at 50 yards. I don't have it anymore, since I lost it in a divorce, along with every other worldly possession in 1984.....
Solid wadcutters have never been as accurate at target velocities as hollow base wadcutters, in my experience. The hollow base bullet has such a long bearing surface, and obturates so well with the light powder charges, that it's hard to beat for barrel fit.
The bevel base bullet was invented to facilitate loading in automatic loading machines. The bevel just slips into the cases easier, but isn't as accurate. Flat base pistol bullets will almost always produce better accuracy, but the average shooter, who is shooting minute of pop can, will never notice the difference. It's only when you put them on paper that you see the difference.
One of the most accurate HBWC bullets for loading is the Remington 148 grain. It's a pretty ugly bullet, but it shoots really well with the proper load of bullseye under it. Just seat them flush with the case mouth and give them a medium roll crimp, and they'll punch nice round holes in the target where you point them all day long.
In matches, I used to use either bevel base or flat base solid wadcutters for the 7 yard line, since you're just cutting one hole at that distance anyway. At that distance, it didn't really matter what bullet we used, but when you went back to the 25 yard line it did make a difference. When you got back to the 50 yard line, it really made a difference, and there was no matching the HBWC for accuracy.
I was never in the Governor's 20 when shooting, but I was in the top 100 in the state. My best on the team target was 300 - 54X, and I couldn't have done it without HBWC bullets. My best individual score was 595 - 42X, but I was a lot younger then and my eyes were a lot sharper.
The bottom line is, if you really want to wring the best accuracy out of the .38 special, then 148 grain HBWC bullets are what you want. Right after that would be flat base solid wadcutters, and then bevel base solid wadcutters.
You can get good accuracy from all three, but the HBWC will give you the best.
Hope this helps.
Fred