Well, on Hard, you should be able to beat the instant detection threshold with just cave hopper stealth overcoat, balaclava, ninja tabis, cloaking device, and a food buff. So you should be able to mine the floor in the southern part of the upstairs map like it's a wartime DMZ. If you don't have all that gear yet, you may even pick up a level while you go get it - if your build can afford to put a few points in stealth, all the better. Once you're all mined up, bring a bunch of grenades and leverage the "sufficient quantities of fire solve all problems" approach. If you have Grenadier, it'll really shine here.
If you're having trouble on the lower level, all you need are a few gas grenades, a few frags, some adrenaline, and three bear traps, then you'll be clear to get to the tougher upstairs bit. Your double LOS break at the entry to the mall gives you enormous situational advantage. edit: sorry, somehow missed the very clear part where you said you were having trouble up top
Like you, I've never found a purpose for that jackhammer in the Mall. Perhaps it's just there in case you didn't take one of the free ones from Foundry, so you don't have to backtrack? There are a couple uses for jackhammer/TNT in Upper UnderRail.
