Here is an interesting fact. 526 grams of borax decahydrate will dissolve in a liter of glycerol.
I think if you imagine glycerol as a chain of 3 carbon atoms linked together, with each carbon atom having one hydroxide group connected them you can see why.
The hydroxyl groups are hydrophyllic - that's what accounts for the solubility in water of glycerine and for its hygroscopic nature. I suspect it's also what's responsible for its ability to dissolve numerous inorganic salts. It's kind of like having a molecule that's half water, and half organics.
It turns out that the high solubility of borax in glycol is accompanied by formation of boronate esters that will be completely useless as bases. This is most likely to happen when heat is used to hasten solution.
My understanding is that you will not make esters of borax this way, it merely makes a glycerol-borax complex. To make an ester, you'll need to drive off the water to push the reaction along. That means lots of heat - pretty much to the point of boiling. About 240°-280° C - now that's hot! And then at that point, you've made an glycerol boriborate ester, which will be useless for your purposes.
I have learned that there is a glycerol borate. This is probably (I'm guesing, of course) what causes the sudden apparent change in solubility of borax in glycol as temperature reaches a certain point. The glycerol is no longer just a solvent. Is that good or bad or indifferent? Its formula is (C3H5BO3)n.
OK - to make esters, you usually have to have an acid (often an organic acid), an alcohol, and a catalyst. For example, the esterification of acetic acid in excess ethanol (which also will act as the solvent for the reaction) will take place in the presence of concentrated sulfuric acid (the catalyst) and heat. This results in an ester, ethyl acetate.
It explains why I thought my pH meter had gone bonkers.
The reason you are getting lower than you expected pH values for borax dissolved in glycerol is that you are releasing boric acid when the glycerol-borax complex is formed.
Glycerol forms a complex with the borax, forming monomeric or dimeric complexes with the glycerol. In borax, the sodium atoms are surrounded by borons atoms connected to other boron atoms with hydroxides bonded to the borons as well. The glycerol complex liberates som eof those boron atoms to form boric acid as it complexes. This free boric acid is what it lowering the pH of your solutions.
In fact, I once used this reaction as the basis to determine the amount of boron (I was looking for borax) in an industrial product that I was hired to deconstruct - I think there was a bit of industrial espionage going on with that project... Anyway, you can titrate a solution of borax (which is basic) with sodium hydroxide (also basic), using pH 7 as the endpoint.
Think about that for a second - you have a solution of borax with a pH of 10 or so, and you titrate it with sodium hydroxide with a pH of 13 or so - how do you get an endpoint of pH 7? (Isn't chemistry fun!?)
The simple way is to add an excess of mannitol (a sugar alcohol with a structure rather similar to glycerol) or glycerol to react with the borax. The borax releases boric acid as a result of the excess glycerol or mannitol. (Neither glycerol or mannitol have much effect on the pH of the solution.) You add some methyl orange or phenolphthalein indicators and titrate to the endpoint of the indicator. The amount of sodium hydroxide used in the titration is proportional to the amount of boric acid liberated in the complexing reaction. You can then calculate how much borax was present in the original sample.
I can list the chemical reaction equation if you like.
So I'd say by dissolving borax into glycerine, you are liberating boric acid and consuming your borax. Probably not what you are really trying to accomplish by using the glycerol as a "solvent".