...... But 6D is just too big for a camera to bring along always. Its just too professional to bring with. ...
I feel quite the opposite, 6D is just too professional to leave behind.
If you swap your 35mm f2 IS for a 40mm f/2.8, the assembly becomes ~1.6" (40.8mm) shorter and therefore less too big.
Suggest you try a 40mm on your 6D at a camera shop, see just how small the pair actually is while keeping all the full frame goodness.
6D, 40, 50 1.8 II, 50 1.8 STM, 24-105L, 90EX, 2X 600EX-RT, 2X Lightsphere, ST-E3-RT, Kenko DG set, GT2531LVL, Ultimate GP, PRO-100, SPYDERPrint, MG3122, PA242W-BK-SV, Intuos Pro, WIN 10 on hardware with intent, AE-1, D-70, D-80, P30T