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Also, I have no idea how to adjust the stage order but I can fairly easily clear the first four stages in loop 1 without dying or bombing. Are you referring to the loop 2 stage ordering?
Yes, I was referring to loop-2. The stages ordering in the first and second loop remains exactly the same.
There doesn't seem to be any extra bonus for collecting bombs on full stock (as far as I remember), but there is a significant bonus for each life+bomb saved after you clear the second loop.
So what I was simply saying was that if you intend to play game long enough to get a no-miss clear(with few bombs), you would want to choose Fortress/Desert + Sea,Sky(these two in any order). The reason is simple. Once you learn the first loop well enough (which is just a matter or time and knowing the tricks to dodging the more unintuitive attacks), you would be entering the second loop with full stock. Since the Fortress stage (followed by desert imo) is hardest it makes sense to include it early so that any bombs you would lose, you can later recover some of them.
Simple example is you entered the second loop with 9 bombs and you play sky/sea/desert/fortress. You would have 9 bombs entering the desert boss (assuming perfect play on sky/sea). Assuming you use 1 there and 4 on the fortress stage, you would be left with 4 bombs. Add 1 that you would be getting in the stage(fortress) and upon entering 2-5 you will have 5 bombs.
On the other hand, suppose you choose fortress/desert/sky/sea, and enter with 9 bombs on second loop. Used 4 bombs there and left with 5. Used 1 bomb on desert boss (leaving you with 4) and played perfect on sky/sea (again). This way you would be entering 2-5 with 7 bombs (counting 3 you get on stages from 2 to 4).
I am assuming above that you get 1 bomb per stage, but I don't actually remember though. As for stage order, in arcade version it seems to change upon reset. So you can just make a save-state early, quickly go through levels 1-4, and if they are in desired order, keep the save-state and otherwise discard it.
But all that only matters when you are refining your play after a second loop clear. I have been too used to default order and even if I went back to this game(for a better score), I am not sure I would change it even knowing that it means less end-of-game bonus.
Not sure if the console version you are playing has stage select, but good luck trying to clear it without save-states. I expect it to be very hard. And especially, if the game doesn't have stage-select practice for second loop.
Probably even with stage select for second loop, I would rank a simple second loop clear (using bombs/lives freely) without save-state practice to be slightly harder than a no-miss clear (with save-states). And without stage-select probably I would rank it much much harder.