Well personally, I rarely use my right thumb on my two-hand playstyle (unless it's a three-note chord).
Anyways, all that I can say to you is that it's up to you whether you want to use thumbs or not. It's just that using thumbs makes it easier for you.
Simply put.
As for one hand play, what you need more is a "STRONG RING FINGER". I tell you, with that kind of ring finger strength, you can go far (far as in clearing Indigo Vision or even Alfarshear's scale frenzy)
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