Thank you Lee for the professional consult.
What I'm understanding is that I will need to get a wire from the panel in my kitchen to the outside of my house and the antenna ground rod. Honestly, I don't think this will be possible without any sharp bends as it would have to negotiate quite a few wall corners to make its way outside. I would also doubt the ability of that gauge of wire to be fished through the studded walls without ripping them apart. There is a female who would not be onboard with demolition.
If the panel is on an exterior wall, you might be able to fish it (or a small string or rope, since more flexible) using an insulated fish rod up and through a bottom panel knock-out. You could then connect your antenna and radio grounds to the rod outside and run them up to your equipment and go through a wall upstairs, if on the same side of your house. If remote, you might have to use the attic to route it across and down to the room where your gear is.
If this is not possible, what is your opinion of connecting the antenna's feed line to an isolated ground rod with a second run of feed line into the house - the feed line would be disconnected when not in use, physically / electrically separating the antenna from the house?
That would be risky, as someone touched on the floating or failed utility service neutral scenario. With underground aluminum service drops that most utilities use today, it is quite common to have corrosion occur which effectively opens the neutral. When that happens, the isolated neutrals will shift due to unbalanced 120V load on them, causing a significant offset voltage from ground. And, with a lousy grounding electrode (like a 25 ohm one) it would be raised as well, since not much current would flow through the ground back to the utility transformer. Then, anything connected to your isolated ground and brought in and connected or just lying close to the elevated service ground in your electrical outlet could have as much as 120V on it with respect to your isolated ground. High risk of electrocution, if that were to occur while you were connecting or disconnecting your feedline to your equipment.