A vote for the Bvlgary here, imho i think it would complement your Speedmaster very well, and since it seems that you like utilitarian watches by the looks of the explorer and the alpinist, it would just fell at home. My 2 cents worth
What about a Milgauss? A sporty watch that can easily be dressed up or down. A preowned one should be in your budget....
Trying to stay in your budget first and foremost, I would be looking for a Rolex 1601 DJ (which should leave you with ~2k in your bank), or would even try to get lucky to find a nice 1803 DD... just in your budget. Good luck.
Get an 18k Longines 30L. Shouldn’t cost more than $1500 if you do some hunting and can be found for a lot less with a little luck. That covers the dress watch and you’ve got plenty of coin left over for the next sport watch.
To be fair, it is not because we did not say we took your budget into consideration that we did not did it. For example the Globemaster and the Grand Seiko can be found within your budget https://watchcharts.com/search?q=omega+globemaster https://watchcharts.com/watch/679/overview