I'm not going to focus so much on the psychological pain because, frankly, I think that when people are in excruciating physical pain, they don't have a lot of extra thought to spare for whether or not things are going well for the rest of the world. Unfortunately for this debate, there is only so much pain a body can take before the consciousness is disrupted to the point that it will shut down. That's why my imaginary victim will also have amphetamines coursing through him. However, I'd have to dose them before the proceedings because there won't be any support for an I.V. drip for very long, heh heh.
My victim will enter this scenario very tightly bound, all over, by hundreds of strands of fishing line, so that their circulation is being cut off pretty much everywhere. The cruelty begins when they are released. Yup, released. Have you ever had an arm or leg or hand fall asleep from having the circulation cut off and then you get that pins and needles effect when the blood starts flowing again? You ever had it so bad that it was painful to even move while the blood vessels where re-inflating? It's like a hyper-sensitivity that can take a good few minutes to go away.
So the victim is released, and gets to experience this nice, full-body pins-n-needles to extreme that feels like someone actually is poking him with pins and needles. While this is going on and the victim's skin is hyper-sensitive, we will string him up by his wrists and begin flaying him alive...let's say with Ginsu knives. Not all at once, mind you: we don't want our victim passing out now, do we? And since we don't want him bleeding prematurely to death either, we'll be so kind as to cauterize the flayed areas with a hot iron, giving just enough time between these procedures for the victim to recover his pain threshold. We'll also pull off his fingernails and toenails, slowly so as to allow him to relish the sensation, aaaand then cut off those fingers and toes, being mindful to cauterize those wounds as well, before continuing with the flaying, including a lovely end to that process by scalping him (we'll keep the smelling salts ready cuz even the amphetamines might not keep someone conscious during a scalping).
Once most of the skin is gone (we'll leave a few low blood flow areas un-cauterized, to be sure he still has enough raw nerve endings exposed), we'll string him back up again and give his exposed nerve endings a soothing spray of water from out nearby garden hose (which would probably feel a little more like a soothing spray of shrapnel, to our dear victim). By now most of the victim's dermis is pretty useless for inducing pain anymore, so we'll have to settle for an ending that involves internal injuries. And although we aren't focusing on the psychological pain, I so no reason to exclude it entirely, so I think we'll wind down this episode of 'Worst Way to Die' by beating our victim the rest of the way to death with his own children, of course killing the children in the process (we'll just assume the kids are still small enough to heft by their ankles like a pillow case, and WHAM! over and over again until their all dead, and daddy along with them.)
Ok, I need to go scrub myself raw in the shower after that debate, and maybe huddle, shivering in the corner for a bit.
As a comment on your method, your victim would die almost as soon as he was doused with sulfuric acid, despite the amphetamine drip, for several reasons. One, the anchor and tubing for the drip would be eaten away by the acid, meaning the amphetamines would stop flowing, but even if they didn't, the victim would pass out and die from the fumes alone, which would quickly seize up the respiratory pathways (especially considering that he is hyperventilating) and stop the heart. So all your victim would experience is having his dong snipped off, followed by a few moments of full-body acid burn and suffocation. Certainly not pleasant, but the trim job couldn't take too long, so the suffering would probably only be...like...ten minutes outs of of your hour. And more importantly, he wouldn't have had to endure that terrifying Bieber music or the knowledge that his family is being killed too. My dude got beaten to death by his family, so...yeah, lol.