Sorry if the last comment was flippant- your suggestion just didn't make much sense to me particularly combined with your stated lack of experience making biodiesel.
You're welcome to make assumptions all you want, but many folks' experience (including my own) has shown basic fuel supplier methanol works fine for the transesterification process. I do suggest you get to know whatever supplier you use and confirm where they're getting their supplies.
You make the claim that one uses less at a go, but the entire process is driven by an abundance of methanol. 2 stage base process will help increase yield and decrease the amount of reagents necessary- as you say it is elementary chemistry- more than efforts to find the purest reagents in my opinion. Use of a reagent grade methanol will not appreciably decrease the amount of pollutants during the reaction as you'll be bringing in a boatload of them with your oil anyway.
While I do appreciate the desire to go with the purest reagents, the reality of what we're working with as a feedstock (assuming you're not buying fresh, purified oil) far outstrips any of our efforts at pure reagents. And you're certainly not getting a chemical report on waste oil.
Now if you're getting methanol with 10% or more water in it then you'll run into problems, but if you're so concerned about purity I'm sure you have a hydrometer around to test (particularly if you plan on recovering methanol) and can reject the low quality methanol should you get it from a supplier that isn't shady. Fuel suppliers would get hung by the rafters if they were supplying 50% methanol as racing fuel.
I would suggest test, test, test to see what you're putting in your tank. The elementary quality tests repeated on every batch will help raise your confidence in both your skill at making fuel and the reagents you can get on the cheap. I certainly agree with your caution in dumping experimental fuel in your car. I was both giddy and horrified when I first did it.