The A1 + 200-600 isn't a light combo IMO,
A1 is 1.625 lbs 200-600 is 4.9lbs (no grip or extra battery) =6.525 lbs
Z9 is 2.95 lbs 500pf is 3.21lbs =6.16lbs
Since Nikon doesn't have a 200-600 yet.. I used the 500pf. I could have swapped out for a 150-600mm =6.13lbs.. which is a little less than the Sony 200-600.
So.. both systems/camera/lenses are neck in neck when it comes to weight.
Advantage goes to Sony for being able to use the camera without a grip.. in the weight and size department....but.. not by much.
This is why It's going to be a struggle when the time comes for me.. personally... to decide between keeping my Nikon gear and buying the Z9 or going with the A1. First world problems ... I know.
I can see me using a monopod as like you.. I'm getting older... with either system/camera. The Sony with now grip and say the 24mm f/1.4 could be a fun walking around combo.. very light. Same setup with the Nikon would be chunky. So many things to consider... lol
Best of luck with the 200-600 trials... let us know what you think.
Hatch