I think I can relate to your problem. When the lens is mounted the dimensions are very similar on every side with awkward protrusions and fragile lens mounts to consider as well.
And I'm guessing you want the camera assembled at all times so you can just grab it out of the bag and start shooting (assuming you shoot the SWA handheld)? so I would suggest also looking into one of those Pro-DSLR holsters, some of the larger ones have lots of room inside both horizontally and vertically (i.e. corresponding to the width and height of the camera body). They have the additional benefit of (usually) looking pretty cheap so that'll fit your criteria as well. I remember SONY making them in all sorts of sizes and they usually give them away here with new camera purchases.
I did struggle a lot with my tech cams as well as there are seldom bags with an internal depth larger than 150mm, which is just too short for putting in a ALPA max on its side. But you'll also have to be aware that any bag which can fit that cuboid is also going to be quite unwieldy in real use, as I've found out the hard way, many times.
If you need a large shoulder back, then I also recommend looking into the ThinkTank Video Workhorse 19. When fully loaded it is again an unwieldy bag but if you're working from your car (or very near it) or you have a suitcase to roll it around on, then this one is killer. It has skid-rails on the bottom and has an internal aluminium frame to maintain shape and also protect the gear inside. As someone who's often going in and out of buildings trying to get to rooftops, its best feature is that it won't attract any unnecessary attention.
But if a backpack is what you're looking for and you have multiple setups (less, backs, accessories, etc.), then I must agree with most here, the ICU system with F-Stop (or similar brands, you know) work very well, it's what I always come back to after trying so many different bags (Crumpler, Manfrotto, Vanguard, LowePro).