Mobile Scanner Antenna
I just got a Laird, tri-band, closed coil (receive only), the all black model. How high is your luggage rack, this antenna is about 18 1/2" overall mounted without the spring base. NMO through hole mount gives me the added function of a ground plain roof. It cost me $28.97 shipped to my door. The scanner is a Uniden BC-15X. Everything about an antenna is a compromise. The laws of physics dictate the length of the antenna for you application. If you can make up the distance desired by lowering the mount to the roof, you will be satisfied. Since this is a receive only antenna, no worries about RF radiation and this antenna has great scanner coverage. I'm hitting bands that were silent before including CB and 800 mhz.
Another thought would be replace your existing AM/FM antenna with good scanner antenna and just split the signal with the AM/FM radio. I would have done this with this antenna but I already had an extra NMO on my roof. Remember, without a good ground plain, you're only getting half the goody out of you antenna.
I am not an expert on antennas or scanners so any corrections would be greatly appreciated by all parties concerned.