My 340 is running hot I think.. I need a sanity check.

Just a little something I'll toss in.

No, the heater hoses will make (almost) zero difference in the cooling of then engine.
Make sure your cap doesn't have any little cracks in those two rubber seals, as you are actually using a recovery system type cap.
And that my car runs 195-210 regularly on hot days and I'm fine with it, and I run a 190 stat in it.

If it gurgles and/or pukes fluid after you shut it off is when you start getting concerned, and in my own opinion they should all have a coolant recovery system to keep as much air out of the coolant as possible.
I made one out of a Shotgun shell looking thermos and plumed in from the bottom so it is nice and clean looking and IF it ever pushes coolant out and overflows the bottle it also comes out the bottom because I drilled a vent hole between the two inner metal layers of the bottle.

One other thing to mention is drilling a 1/8 air bleed in the thermostat solves the air bubbles when filling problems.

Not that you haven't done any of the above, but just notes.