An antenna tuner will not fix the real problem, it will only fool the radio into thinking it is ok.
Just for reference sake, an antenna tuner does fix the real problem. It is an LC network. So it matches the transmitter's impedance to the feedline. The real problem is that a dipole is a balanced antenna so it needs a balanced feedline if it is not at resonance. With the antenna at resonance, the capacitance and inductance values of the antenna are equal and you are dealing with pure resistive values.
Coax is not a balanced feedline. If you do buy a tuner, buy one with a balanced output and use air-insulated hardline instead of coax. Problem solved. It doesn't matter what the impedance mismatch is between the feedline and the antenna in that case because the losses on parallel feedline is so low as to be negligible. On a CB rig running only 4 watts on the carrier, you could probably get by with 300 ohm twinlead from the tuner to the antenna and it would work fine.
The biggest problem with that whole "solution" is that a good tuner costs more than the most expensive CB radios. And you don't really need a tuner because a tuner is only really needed when you intend to run a particular antenna on different frequency bands.
The biggest problem with the antenna in this thread is that it is a balanced antenna with an unbalanced feedline. So the easiest solution is turn the antenna into an unbalanced antenna by converting it to a ground plane type with the ground plane grounded. And then it will work fine.