There is your clue, you said "old TV coax" which is unreliable at best & splitters which subject your scanner(s) to additional db loss. I would venture that Dave, a member of RR owns DPD Productions which feature the "Custom Blade" VHF indoor antenna should solve your problem with minimal cost & aggravation since your listening preference is 145. to 160. MHz, this antenna could be tuned to the center of that band, it already comes with 18' of RG8X with a BNC connector already attached. As for splitters, I never used them in any of my scanner set-ups, there are economical, inexpensive & expensive splitters available however you get what you pay for, each scanner and receiver I've ever owned had it's own antenna as it alleviates a lot of problems such as if the antenna malfunctions, now you have two scanners out of action, to familiarize yourself with such systems check the WIKI section. Maybe someone reading your post will have a more viable alternate solution to your dilemma.
FLRAILMAN
DPD Productions - Antennas & Accessories for the RF Professional & Radio Hobbyist