I'm pretty sure the problem is that you need a (rare, but presumably cheap) manual-to-auto swap, or a driving lesson.
What you are doing is called lugging the engine. You are basically hammering the living crap out of every moving part (and most stationary parts) between your intake manifold and your tires.
This happens when you try to drive at a lower RPM than you have the power for. Instead of working smoothly and staying balanced, the individual cylinders do not have the ability at that RPM to move as fast as you're asking them to, and the combustion simply puts a huge shock into your motor, and yes, into the rear end as well, given that it's all one drivetrain.
Additionally, the bearings (and other parts) are protected from metal-to-metal contact by a film of oil, which is why your engine works for more than a few seconds before self destructing. I personally find it quite likely, though I know of no evidence that I can cite, that the oil pressure, tuned to increase as needed for smooth operation at a given RPM, is not sufficient to prevent metal-to-metal contact when you lug, and so when you do, you're really screwing up..... everything.
My personal ka, admittedly not a perfect specimin, does not like to cruise below 2k, or accelerate hard below 2.2k or so, in fifth. It starts lugging hard without even accelerating when it hits about 1.8k.
Anyways, my point is that you're ruining your motor, and trying to blame your bushings. It may be possible that when you're lugging it's ALSO setting off bad bushings, but jesus, your way of finding out what's "wrong" with your car is to go and try to wear it out as fast as you can and listen to it.
When you're engine braking, the differential and rear end reverberates some, and you may have a different exhaust sound, a bit of a roar. But that's something else. As long as you don't touch the gas, it's okay to engine brake down to idle, as long as you clutch once you get there, as far as I know.
this thread sums it up pretty well. "Try riding a multi-speed bicycle up a hill in too high a gear and that is a good way to think of lugging. You'll kill your knees and have to downshift. Something has to give."
Sorry about the long post, but I'm worried for your car's health. Maybe you should find a civic or something.