OK, let's make sure you understand glycerin first. It will help speed trace(something you
really do need in liquid soap). It will not thicken your soap. You need to first learn to make liquid soap paste before we can move on to thickening, as thickening is done primarily after the soap paste is made.
I ran your recipe through SBM at 3% superfat, and got KOH-6.91 oz and Water-20.73 oz. Using those numbers, what I would do is this:
I would mix my KOH into 10.4 oz water until dissolved, then add 10.33 oz glycerin to the hot KOH/water mix.(50% water, 50% glycerin to get total water amount of 20.73) This is my personal preference because the math is easy and sort of idiot proof.(me and math are not friends) However, I have successfully used as little as 1/4 the total water amount in glycerin and still got a faster trace than using plain water. So, while I would use more than the 1 oz you originally thought, you need not use the whole 20.73 oz in glycerin. This saves lots of money while learning liquid soapmaking.
You can add that glycerin to the batch oils, or to the hot KOH/water. It does not change the outcome one iota. Just remember to get it in there before you start stick blending. You can't add it to the borax water, because that is dilution phase, not paste making phase. Got it?
Now, thickness of liquid soap is a huge issue. On this one, I will send you to read IrishLass' tutorial in this thread:
http://www.soapmakingforum.com/showthread.php?t=46114&highlight=glycerin
And the follow up in this thread:
http://www.soapmakingforum.com/showthread.php?t=49852
Because I can't seem to get my paste and diluted soap to come out that perfect gel consistency. If I were you, I would use her recipe exactly as written until you have a few batches under your belt. Do read her posts in both threads first, as she does some experimentation that you need to be aware of.
Please note, however, that she does not use borax. I don't use borax either. Most of us do not use borax for various and sundry reasons in making liquid soap.