Fighting the 'teers early is something that's already documented, but I figure I'd mention that I squeezed my way into that as well (and I also Polar sniped).
Regard health, I finished with 27 HP (so I found 24 of the possible 37, according to the FAQ), and I didn't miss any HP in the original Cave Story, not even the first time through. Considering that I've gained experience since then, I'll guess that you cranked up the difficulty a bit much. Instead of maybe hiding so many capsules, maybe make some of them just moderately tricky jumps. They don't even have to be silly hard like the one on the right side of the Mimiga village.
Regarding Monster X, it is possible to get all the way across without Monster X. The "tricky" part would seem to be crossing the second set of spikes (they are all -127), but there's a place where enough of the spike is covered that you can stand on (you're still halfway through the spike, but it's not enough to trigger damage). Anyway, does the column of spikes serve any real purpose other than force you to take damage? You're killing someone's hope of pulling off a 3 HP run.
Regarding weapons, well, this may take a while. First, some ammo progressions come to mind:
Snake: 50, 60, 70 (up 20% of the original at a time)
Bubbler: 25, 50, 75 (up 100% of the original at a time)
These may be more suitable at 40, 60, 80, or 40, 60, 80, 100, or 50, 75, 100, or some other nonsense (in other words, aim more for like up 50% of the original at a time, maybe as low as 1/3 or as high as 2/3 if the starting value warrants it, like 25 or 30; 1/4 and 3/4 are pushing it, but sometimes those are what you need). The Snake ammo number seems a bit on the big side, but I guess it can't be helped; after all, the Bubbler recharges, but the Snake doesn't.
It would seem very difficult, but it's probably possible to skip the Snake and instead pick it up after losing your weapons. Be wary of that.
Regarding weapons after you drop them, having just the Bubbler and Missiles is a bad combination. A rule of thumb I believe is to be sure the player has unlimited ammo that can destroy blocks (at least when they must destroy blocks to advance). The Bubbler can't break blocks at Lv2 or lower, and Missiles are limited. This wasn't a "problem" for me, but it can be very inconvenient.
Also, and this applies to HP as well, you don't want to penalize a player that doesn't know the secrets as much as reward a player than can find them (but since they are usually extremely skilled/determined, you don't want to reward them too much). Giving the player a Fireball takes the 'teer fight from insanely hard (especially without the Sword, since your Bubbler becomes powerless in a hurry, and Missiles are extremely limited) to painfully easy (just have stand on the blocks above and spam without mercy). This is NOT the kind of reward a skilled player wants (heck, the original Cave Story rewarded skilled players by giving them a harder final cave and then allowing them to play Sacred Grounds).
And even in general, and this has been mentioned already, but the Bubbler's quick de-leveling makes a Sword-less and Fireball-less player powerless in a hurry (aside from ~15 missiles). Maybe swap the contents of a 5 missile box with the Sword or Fireball (although I know you have the Sword scene set up already). Or maybe give the Machinegun in place of the Bubbler: it may be overpowering, but it makes the 'teer fight playable (even taking one hit saps any unf the Bubbler might have, and no Fireball means no brainless spam).
Finally, whenever you have a secret, you need to give a solid hint. You can be subtler than the block which hints at the Arms Barrier in the original Cave Story, but don't force the player to investigate every single wall (that's just boring). I even read your hint about the Blade, and I still have NO clue about where to fall/jump to get it; and if you're going to hint that a secret path (or if you in fact make a secret path) is around some dangerous area (like spikes), have a save point not too far away. I'm not daring enough to risk death after a lot of trekking, especially when I'm skeptical there's a secret there anyway.
So yeah, you can probably tell I didn't find the Fireball, either.
A final idea that comes to mind in the 'teer fight is to change the terrain so that a person can't just snipe. This isn't just from the left or right, but also from above. You may need to decrease the difficulty of the fight in some other way to compensate (damage taken per hit, decreasing enemy HP, decrease the rate of projectiles fired at the player, maybe allowing the player to hurt *all* 'teers at any point in the fight as opposed to just one at a time).
It's a great mod, and it's coming along well (a lot of the earlier parts have been cleaned up well), but it'd best to agonize over every single detail now rather than let hoards of players do that later.
