I read further into your posts and I caught this...
...[...]...
EXCEPT... (this is where it gets weird). Assuming the radio swr meter is a way to see a rise or fall in reflectivity back into the radio, which is spiking up and causing my radio to go into swr protect mode, when I leave my property and get a quarter mile down the road, everything works as it should. I tested this by driving to town this morning and just happened to try it having spent all day messing with it yesterday. Radio swr never got over 1.5 when I was away from my property. The closer I got back to my place the swr rose back and when I pulled in the driveway it went back into swr protect mode. I’ve got some very strange happenings going on here. Maybe this is where they are filming “Stranger Things” season 4???
That is a good way to look at this - "Stranger Things" ...
I think we may have answered the question when you said you started to drive away...
That usually indicates the Alternator is now putting out enough current into the system to top off the battery and offset the voltage drop that amp starts to draw down using the system...
It affects your deadkey as well as voltage drop - a simple drive under load, wham - the alternator kicks in to offset it.
So the "drive away" and then the slowing down of the vehicle to your neighborhood ...
Seems to tell me you issue is you need more RF power from radio - D/K to amp related.
So that means Amp and Radio - check and see...are votlages ok? I mean seriously - tap the + of the radios own power lead with the DVM RED, and the + of the Amps power lead using your BLACK (negative), leave the DVM in in VOLT setting 20v to try and then less to obtain more SENSITIVE readings, and key the stuff - if you get more that 2 volts showing on the meter that is your DIFFERENCE between the Radios' Power Feed potential and the Amps Power Feed Potential - if one drops more than the other - 2 volts or more - you need to fix that drop.
Can you bump up D/K in Radio to offset the SWR - as a test to see if SWR improves faster...
If the higher DK seem to make your SWR better as in, to "stop shutting down your equipment" - that goes back to the voltage drop the amp has - on itself, because it uses a relay and buttons to route RF as well as power the pills. So if the amp "stutters" as you key up your radio - naturally the SWR will jump - it's not foolproof.
A little extra AWG wire onto a better route of wiring to that amp can help a lot in this case...
You may have to go under the hood of that amp and look for ways to make it more sensitive to input. That may mean removing the RF sense and using direct key to make the relay kick. I'm thinking the amp either by inherited design, or tuning done to it, is not catching all the RF the radio is sending to it, thru it's (amps own) input network - simply because of the heavy class C bias. Tends to force clipping of the signal until it's strong enough to force conduction. You may not have a choice here. Either bump up the DK and run a little more limiter or the amp needs to little more work on the input side to make it more want to amplify on low RF signal - else with heavy class C amps, you really have to push a watt or more to get the amp to at least be linear and amplify what it sees.
This is not a diagnostic, but then - if the relay is old, that can have an effect on your stuff.