Not trying to duck your question here...
I assume your two wires are physically kept close together by something like glue , or their innate rigidity ? If not the geometry will change and the problem becomes dynamic.
I'll answer that each wire will experience a vertical force from its Lorentz
force effect and those forces of course sum to zero. (ignore the torque couple for now)
and there's an additional force on each wire from the other one
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/wirfor.html
of course you postulated current in opposite directions not same direction as in this figure - so wouldn't that force be repel not attract ?
I've been thinking nights about your questions
and they make me ponder what is nature of space that force is transmitted between objects over a distance by magnetic and electric and gravity fields?
Higher math is able to describe the interactions out there in free space not just at the objects.
But we can only sense the resulting force at an object like a wire or a charged piece of matter where we can attach a force measuring device..
I need an aether.
I think that's why i stick with my 19th century analogies - my algebra is so prone to mistakes that i have to visualize the forces before i'll believe the math.
That is a handicap. I really advise you to master Vector Calculus and Maxwell's equations, they've become the coin of the realm.
old jim