Note...increased snap/spin will not help a disc turn-over! More spin only stabilizes the disc and makes it difficult to turn, no matter if it is right or left. This is simple physics.
Off the top of my head, there are 5 potential elements to making a disc turn right...
1. Anhyzer. Release the left edge up for RHBH throws, setting up the disc to already turn/roll right. This can be accomplished by a slight downward motion on the forward part of the throw, which makes your wrist bend slightly up and lifts the outside edge of the disc prior to the snap/release. I've also seen players lean back slightly instead, pointing their chests slightly higher in the air. Try something along these lines, and it'll start turning right almost immediately.
2. Nose down. A nose down release pitch to the disc causes the tail of the disc to have more aerodynamic lift than the front of the disc, which induces a torque that causes the RHBH thrown disc to turnover/roll even further to the right. (A spinning gyro-top toy works the same way, with gravity instead of air supplying the torque.) I usually get the nose down a tad further by orienting my thumb slightly down during the entire throw. The above-mentioned slight downward motion of the disc during the throw can also help get the nose down.
3. Speed. The aerodynamic torque-roll effect described for #2 is stronger when you throw at higher speeds. The faster you throw RHBH, the more the disc will roll right. (Note that big arm throwers need an overstable disc or more snap/spin to prevent catastrophic turnover/right roll.)
4. Under-stable disc. An under-stable disc has more natural tail lift relative to nose lift and will tend to roll right by gyro-precession action all on its own when thrown the same way as a more over-stable disc. (Under-stable discs can be identified by sight as having a larger central flat area on the upper surface, as opposed to a big curvey-dome-like shape with no/little flat patch at the center. In the most under-stable discs, like the Stratus, the flat central part of the upper surface covers most of the disc area out to nearly the edge. In more over-stable discs, like the Wraith, there is almost no flat patch at all in the center of the upper surface.)
5. Less snap/spin. While not recommended, for stability's sake, less spin can actually help a disc roll right (or left) by reducing its angular momentum, or resistance to turning by torque. Less spin means less aerodynamic torque is required during flight to make it roll over further.
I would strongly emphasize 1-4, and avoid fiddling with 5. Getting and maintaining a good snap is always a good idea, and as you can see from the above list there are many other factors can be adjusted to make a disc fly the way you would like without messing up your release.
Note that if you take the above elements to the extreme, the disc will turn all the way over sideways, drop to the ground, and become a roller...these kinds of shots can also be very useful.
Try it out, and have fun!