First of all, hang in there! You are certainly not alone in your feelings.
My only advice is to consider a "no-fit corner". People have told you to put him in time-out for whining but that won't work because a child so young simply does not know how to turn off the water-works quickly. A no-fit corner is completely different, though. It should be someplace different than the time-out corner and it doesn't have to be a corner at all, just someplace quiet and out of your line of sight.
When he starts throwing tantrums, explain to him that he's going to the no-fit corner to cry and he can come out when he's done. This will allow him to express his emotions (which is natural for a child his age) without getting any attention from you.
When he comes out, ask him if he's done and give him loves. DO NOT, of course, give in to what he was originally throwing a fit over.
If he comes out still crying a little, that's to be expected. Like I said, it takes kids a LONG time to turn that off. But if he's still throwing a fit (shrieking, etc.) tell him he needs to go back until he's finished.
This is a fantastic way to work through the "fit" stage.
One thing, though...every child develops differently and your son might or might not be able to grasp the concept of a no-fit corner. Since you said he responds well to short time-outs, I feel like he will do fine with this "new" corner, but ultimately it's up to you to determine if he's ready for it.
Best of luck to you, Sweetie.