Just a suggestion: try the dipole without a balun for a while, just to see how it behaves. I know what the books say about a balanced antenna with an unbalanced feedline, but none of the coax-fed dipoles I've made in the past 52+ years has needed a balun.
This is pretty strong testimony!
You know - Your right - Just string the dipole between two trees and do not even worry if you have it measured correctly . Use a tuner and stop worrying about the little things.
That is just what I did in my early days of ham radio. And why the change ? Well because I think there is a better way.
This is what I suggest - Get a DXEngineering catalog and go to page 33 . Look at the pattern of a antenna with no balun and one with one. Read the simple explanation they have on the reason to use a Balun verse not.
Honestly - You will work station with out a balun .And frankly if you want to use nothing more than a 150 watt light bulb and you will work stations sooner or later. But there is better antenna and systems to use.
All my yagi beams use a balun - My super loop 80 - my 160/80 T's has a 1-2 Unun at feed point in series with a 1-1 balun. The tuning is separated from the coax by a 1-1 balun Made by Balun Designs LLC.Made by KZ5R , which is W2FMI design. Solid RF engineering at its finest. I will argue with any one on this one.
I have in fact tested perhaps more antenna than most hams in this area and every antenna I ever used I worked dx with them. But that don't mean they were all efficient.
I do view this as a important topic best of luck