RW,
You are quite right about the Omega 8500 movement being extremely consistent - technically this is called isochronism, and is not the same as accuracy. A watch that is say, consistently 10 seconds fast per day under any conditions, has perfect isochronism. It also means that in the hands of a competent watchmaker its accuracy can be regulated to within 1-2 s/day. If a watch with good initial isochronism is properly regulated, you get what your AT 8500 does - and so does mine, gaining 1s/week, regardless of anything. The ETA 2892-A2 is not that good, variations of 2-3 s/day in isochronism either way are not uncommon. But it also depends somewhat on luck - my Aquatimer 3548 is actually dead-on, also regardless of anything.
Whenever I got a new watch - or even a pre-loved one that has been sitting idle for some time - I found that it could take the movement as much as three weeks to settle in a steady rhytm. My Ingenieur 3239 started off by being +3.5s/day, but after three weeks is now +1s/day. If you are obsessed - and I stress the word obsessed - with both accuracy and isochronism, you should try to find a local watchmaker who can regulate your watches according to your feedback. But beware, if you change your wearing habits or level of activity, you may need to have it regulated anew.
If you can take a few words of advice from someone who used to be as obsessed by accuracy as you are: when you get a new watch, by all means, check its performance for a few weeks. If it performs within plus-minus three second per day (my own COSC standard), leave it well enough alone and enjoy it for what it is. Or just go and try to have it perfectly regulated, but know that, in the words of King Lear: "O, that way madness lies."