I used the stock antenna on the radio. I could hear the airport sporadically, but it was very faint. I can hear much more of the airport now. So there was a gain there, but no real gain in the 750-850Mhz range.
Well, as stated above, the discone antenna has zero dBd of gain, which is equivalent to a dipole. You are loosing some of the received signal in the coax, and that's normal. LMR-400 is pretty good for this sort of application.
If you want better 700/800MHz reception, you might want to consider a dedicated 700/800MHz antenna, which will have some gain.
Or, add a preamplifier, and/or better coax.
The antenna on top of your scanner may not have been a good performer, but there was zero feed line loss. But down low in your home, it's going to suffer.
This was mainly a test prior to placing the antenna outside. However, if I understand the grounding best practices correctly, the antenna coax should from the mast, down my house, into a single point ground, and then back up to the attic where my radios are. I'm estimating that this is 75 ft round trip, so it doesn't sound like there's much to gain from it (unless I get a higher gain antenna).
Mounting in the attic isn't always the best choice. Some roofing materials/insulation/etc. have metal in them and that will block your signal. Even if it's just wood and shingles, there's still some attenuation. Getting the antenna outside and up as high as you safely can will likely show improvement.
As for the grounding, I think you misunderstood something along the way. There is no need to run the coax all the way down to ground level and back up to the radios in the attic. Just run the coax from the antenna to the radios. Where the coax enters the house, make sure you install your lightning suppressor. Then just run a suitable size ground conductor down to the ground rod. Make sure that ground rod is bonded to the original house ground rod, probably near your electric panel. No need to waste all that coax going down and then back up….