First all your network stations being to the SW (210 degrees) is good, but they are 2 edge stations and may require a large antenna/antennas. You do have NBC at 245 degrees.
Your only CBS station is on channel 6, so you require either a large VHF low antenna or possibly you can pull it in with an FM antenna since channel 6 is right at the bottom of the FM broadcast spectrum.
Acceptable (and pricey) all channel antennas are out there like the Winegard 8200U, but I feel you would be better served with separate UHF and VHF antennas (both cheaper and better reception) combined with a UVSJ (UHF/VHF signal joiner) and amplified.
I might even go ahead and spring for the 8200U but eschew the UHF part and use an Antennas Direct 91-XG for UHF instead. Channel master 5020 is another all channel all band antenna like the 8200U but slightly less expensive ($160 MSRP vs $190).
If money is tight, just go for the CM-5020 and point it a t 120 degrees.
Winegard 8200U vs. a cable bill is not much cost. Pay it off in 2 maybe 3 months... Not a big deal. My parents get decent reception on a real channel 2 in the 10 to 15 dB NM range, so channel 6 at 27 dB shouldn't be a big deal.
You have gotten good advice. I would not over look the Antennacraft HD1850 or HD1800.
As has been mentioned the wide antenna is a requirement for low band VHF reception of real channel 6. Electrical interference can also be a real problem with low band VHF. If you can live without CBS antenna size requirements shrink quite a bit in width.
I feel I must state the obvious, namely that an outdoor antenna will be needed in this situation. Even an attic installation would be dicey, unless you have plenty of room up there and unusual luck in the building materials of your roof and attic. Also, if there are any buildings to your south-west, or more than one or two trees, that could put the kibosh on the whole idea. The signal is already refracting around two bumps in the terrain, so you don't need any more obstructions.
If I were you, I'd try a few greater antenna heights in the TV Fool Report. Even if there's no possibility of getting an antenna up 40 or 50 feet in the air, I'd want to know if most of those 2 edge signals might suddenly morph into 1 edge. It's hard to tell on the transmitter profiles, because the distance is so great at 65 miles.