Just something built like a tank, so I don't have to worry about having to baby it or things breaking. Want to use heavy nitro loads in it and the ability to use 3" shells.
I can only speak from a UK market point of view but ....... what you are describing is a heavy duty
boxlock.
Sidelocks were (being more expensive and arguably inherently more delicate) used on lighter and more upmarket game guns. The stock around the lock inletting can be a failure point in heavy use. AyA's No 1 and No 2 are copies of the typical English sidelock, but are not heavy duty guns. Models 53 and 56 are heavier grade guns, but model 56 is not cheap, and uncommon in the UK. I don't think either of these has 3" chambers (at least UK versions don't).
The vast majority of heavy duty rough service guns were boxlocks .....strong, reliable and long lasting.
Sidelock o/u guns are uncommon overall, and and very much towards the 'top' of the market. Again, they would be rather more delicate than boxlocks.
I don't think what you are looking for will be easy to find.