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Ok I think I found the first major sequence break.

This trick is actually really easy:  angled bomb jumping.  You drop a bomb, move slightly to the side and are shot up diagonally.  Instantly start spamming bombs, timing is even easier than vertical bomb jumps.  Each bomb kicks you further in the angle you're heading, all you have to do is hold back towards your original position to maintain the angle and the repeated angled bomb jumping.

Get to the large vertical chamber in the far right side of Brinstar where you get the Bomb.  Reach the top of the chamber by using a very long vertical bomb jump.  Hint:  Drop 2 slowly then start spamming them.  You'll pass a statue, and then one of those organic ball things in the lava below you.  (Which you would normally need to use the parasite trick to pass, going the other way.)

In a single hall chamber with a floaty sine wave monster theres breakable blocks in the ceiling.  Use shooting then quick bomb jumping to get on top of them.  Then, starting from the left side, use the angled bomb jump to reach the platform in the upper left, then more vertical bomb jumping to reach the door.

In this chamber an energy tank is in the lava, which you have enough health to grab.  Use vertical bomb jumps to get on top of and then past the pipes in the middle.  Here there is a single self-decaying tile that you must angle ball jump from in order to reach the small slot to the upper left.  This is extremely hard because a little luck is required to press left at just the right moment to slip into the hole.  It doesn't matter where you drop the first bomb on the tile, but it does matter where you move to after you drop it.

From here release the parasites and then take the Varia.
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Well, I'm currently trying it.  It looks like, at the very least, it's possible.  Crap, the lava just killed me.

In any case, approaching from the other side of Brinstar is much easier.  Also, holding down-back seems to lead to better angle bomb jumping.  [sigh] This would be much quicker with the power grip.
I DID IT!

OK, there is a better way to get onto the last ledge. (The one you suggest angle-jumping into from the decaying block).  Instead of leaving it up to chance, hop (using bombs) to the next decaying block, and steadily (no spamming) bomb jump straight up.  If you get the position just right, you just tap left to get in.  Easy!

Now to try it without save states....