So I installed Tyrian 2000 (and played it through again) to see how it was and how it compares to Jamestown -- was it as good as I recalled.
I got used to the floatiness quickly, however, and in Tyrian 2000 you don't need to protect your one-pixel hitbox to such lengths anyway. The hitbox is probably larger, too, but as long as your regenerating shields are up, you're safe. And after they are gone, the ship can still take hits till the armor bar is gone.
However, if that happens and you die, you have to restart the level from the beginning. It can be quite frustrating to play flawlessly through a lengthy level only to get instantly gibbed by the boss who decided to move right onto you. (Shields and armor deplete quickly if you collide into stuff.) I may have ragequit few times because of that.
Occasionally you can get upgrades during levels as well, though I'm not sure if they are permanent. There also seems to be some special weapon slot, which is activated from the same button as your main fire (which you are usually holding down). I had few different ones during my playthrough. Two of them didn't seem to even do anything, as far as I could tell. Such an odd mechanic.