What I really want to know is does the cable need to be in a straight line to avoid being a fire hazard and/or an RF interference magnet, or will it be okay if they run it along the roof and wall of the building?
I'd add that any lightning strike directly to your antenna is going to be a fire hazard, ground or not. You'd be looking at several million volts and a whole lot of amps all trying to find a way between ground and cloud. A thin layer of insulation, paint, electrical tape, shiny new scanner, etc. is not going to stop it. That much juice trying to get where it's going is going to heat things up very fast. Fire is going to be a real risk in a residential environment.
What you are ideally trying to do is to give as clean a path as possible between your antenna/mast and the ground. Some of it will find other paths.
I was on a ship once that got hit by lightning. Lots of antennas, radar, etc up on the mast. No damage at all to any of that equipment. What got knocked out was an engine management computer down in the engine room. Lightning doesn't necessarily want to follow our rules, although we can do our best to get out of it's way. That's really the best you can do.
It sounds like you are doing the right things, and I understand your concerns about wanting to make sure it's done right. NEC requires what you are doing, many scanner/SWL/Amateur radio operators ignore it. You are likely way ahead of the pack. It'll be interesting to see if this has any effect on your noise issues. All I can really say is that none of this should hurt things.