I've just read this thread in its entirety, well skimmed it anyway. Here's my tuppence worth.
It's still early days and things will improve, never doubt it. That Desperate Dan beard is making things harder, and that's pushing you into doing more passes than are advisable. Stick at three for now, maximum. That's plenty with a nice smooth straight razor, let alone a DE blade, so two would be better for your skin's sake.
All very well, you say, but I'm not clean shaven. Well, there are a number of things which may be hindering that, starting with preparation. Lying in the bath with a hot flannel over your face for as long as it takes to read a decent newspaper is over the top, and well worth trying. Obviously not one for every day, but it's a worthwhile experiment because you can be sure that your beard will be as soft as it's going to get. Slapping on some lather or Proraso pre / post beforehand won't do any harm either. Lather up, taking time to make a good job of it, then find a displacement activity for five minutes or so, which should include installing a brand new blade into your razor. Adjust that lather, then shave slowly and carefully paying attention to the angle, using just the weight of the razor - no pressure. Two passes with the grain, no going back over where you've already shaved, and stop right there. Warm rinse, thorough cold rinse, apply one product of your choice. Follow all that to the letter, and tell me the shaving experience isn't better.
Now that was all very well, but it's not practical, I know. The point is to hammer home a few basics:
1) Don't stint on the preparation. Hot water is your best friend.
2) Two passes (or even one) done to the best of your ability are much better than umpteen increasingly desperate scarifications in search of the perfect shave. BBS or whatever you want to call it is certainly achievable, but not worth chasing at the expense of flaying yourself and feeling discomfort for hours afterwards.
3) Rinsing thoroughly with cold water is important and extremely effective. For many years that was the sum total of my post shaving routine and it works as well as anything unless you want to add a scent. That can be done just as well with cologne, by the way.
4) Too many lotions, unctions and so forth applied together just cause trouble. High alcohol splashes or witch hazel work best for me; alum, balm or something like Proraso work well for other people. Find something that suits by trying them one at a time.
Eventually you'll find a routine which suits, and you'll hone your method to the point that you can make yourself socially acceptable in five minutes - trust me on that.
A word on hardware. Modern safety razor blades come in quite a variety, but they are all quite harsh compared to the best blades of yesteryear. In view of your tough whiskers you should be looking for a relatively sharp blade in the end for efficient shaving, but bear in mind that they are hard on your face. For now I'd suggest steering clear of the most aggressive blades, specifically Feathers, and sticking with something like the red IPs which are at least smoothish (sort of).
I'm no fan of timid safety razors (a New, an Aristocrat Jr, or a Slim set to "kill" is the sort of thing which I like), but they do work. Get the prep and technique right and a mild shaver like a Tech will get you just as clean in the same number of passes. My suggestion is that you stick with what you've got and learn to make it do the job, then ring the changes by all means. An "aggressive" razor is not necessarily the answer.