Just my opinion, but liquid soap is drying due to the blend of fats in the recipe, not due to how much or little glycerin you add. Soap made from fat (as opposed to soap made from fatty acids) creates its own glycerin, whether the soap is made with NaOH or KOH.
The main benefit of adding glycerin to liquid soap is to jump start the saponification reaction, compared to using water. As far as the overall performance of the soap after it's diluted, I think a higher glycerin content slightly reduces lather. I personally don't see any great difference in how a higher glycerin LS feels on the skin versus a low- or no-added glycerin LS, but that's just my opinion, not necessarily true for everyone.
If you use a lot of coconut oil or other high myristic-lauric fat, a fairly common tendency in LS recipes, you're going to end up with a more drying soap. We see this in bar soap, and it also happens in liquid soap. I think people crank up the coconut % to get a faster lathering soap, but there are ways to compensate for that even if you keep the coconut down to a reasonable amount.
How fast and how much lather is created depends on the amount of dilution and aeration as well as the blend of fats in the recipe. Foamer bottles are good (aeration and dilution). Or being okay with a more watery, more diluted soap (dilution). Or shower poufs (aeration).
Be careful with the superfat in liquid soap. I gather you intended to have 6% superfat? The rule of thumb is no more than 3% superfat. Much higher than that and the free fatty acids may separate out of the soap.