I’ve always constructed any dipole so that each side is of equal length. Last night I decided to try lengthening just the “hot” side of the dipole using clip leads of various lengths. I can easily lower the resonant frequency anywhere I want it, and the bandwidth remains the same.
I would keep the dipole legs the same length, balanced. It's usually best to do any job "textbook" all the way through. When every component is "textbook" there are no odd variables, rather, everything works together as it should and adds for maximum results. In this case, less feed line radiation - this can reduce a whole new set of problems. Be sure to use ferrite cores and/or a hank of coax coiled up at the feedpoint as a choke balun
After doing it all textbook, if the overall performance is not right, only THEN start JSing around to see if things can be improved.
In your case, as you desire, put up a "perfect" dipole and use a tuner to improve its bandwidth match to the transmitter.
BTW, the loading coils are a great idea since you are using coax and need to get that center impedance up for a good match. The tuner will not help your coax losses, but will give the transmitter a nice match to work into.
T