I do not believe adding a rubber coating to the roof would be of any benefit. It would only increase the distance between the metal in the roof and the foil under the magnets that capacitively couples the vehicle body to antenna ground. Since you already have a hole drilled, adding a ground strap from the mag mount to the roof might help, but it should be as close to the base of the antenna as possible with as short of a strap as possible.
Although I do not have enough info to say that your problem is with the grounding, it is always good to make sure that your grounding method is effective before trying to make adjustments elsewhere. Not all mag mounts are created equal. Sometimes the foils under the magnet are not connected to the antenna ground and the little the foil edges overlap with the magnet housings is not enough for the RF to capacitively couple to the vehicle body. I've used copper foil tape on the roof before, but since you are not against holes, just add a strap.
Was the ice on the antenna too, or just the roof? I would assume that ice on an antenna would be like adding a dielectric coating to the antenna, which should make it electrically longer due to the slightly slower velocity of propagation. I am going to assume that you previously tried making the antenna longer and the dip wasn't getting the SWR that low, so the answer probably lies with making the antenna electrically longer while somehow compensating for the effect of the increased distributed capacitance to ground.
In my experience, running a short antenna on a mag mount usually involves series and shunt inductance, but your antenna only has series inductance. If you had an antenna analyzer or nanoVNA. it could tell us exactly what is happening.
I would recommend getting a cheap nanoVNA and an SO-239 female to SMA male adapter. Then, using a pair of PL-259's from old scrap radios (or buy them), make up some calibration loads for the other end of the coax ~ one as a short circuit and the other as a 50Ω load (these will be used to calibrate out the effects of the coax cable so the VNA reads on the antenna end of the cable rather than at its port). The calibration procedure also uses an open load, but at 27MHz, its not worth attaching, just leave the end open and hit the button. You can calibrate at the VNA port with the included SMA calibration loads if your coax is a half wave long at 27MHz (or you measure it and take that into account), but its easier to make some junk box calibration loads. Once you have done that, connect the coax to the antenna and adjust the antenna length so that the impedance at 27MHz is on the constant conductance circle that goes up to the center of the chart (its the line that starts at the center and goes down and curves to the left). Once it is on that line somewhere, the distance that must be traveled along that line to the center represents the value of shunt inductor that you would solder between the feed point and ground to get your match.
