Most likely the dipole "legs" (wires) will need to be trimmed to get a good SWR. Measure the SWR on the upper end of the band (14.350) and then at the low end (14.000). If the SWR is better at the low end of the band, the legs will need to be shortened. Conversly, if the SWR is lower on the upper part of the band, the legs will need lengthened. That tuner, while a nice one, will only compensate for slight mis-matches and wasn't intended to tune an antenna that is way out of band.
The coax "balun" at the feedpoint is there to keep RF from coming back down the feedline and into the shack, not for SWR purposes.
For verticals, check out the Hustler BTV series. I have a 5BTV at my BOL and with just 4 ground radials it works well.
Oh, I used to frequent Universal back when I lived in the Buckeye State. Are the cats still there?
ETA -- How far from the roof peak/gutters are the wires?