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I thought it could be a select stage mode, but no :)
You've covered everything else. I'm working on the shmups.wiki article for this game, I've collected all this info from experience and experimentation as well as conversations with the devs to get exact values (You might see my name on the credits :D).
Ext 1- 2.5 mill
Ext 2- 5.5 mill
Ext 3- 8.5 mill
Ext 4- 12 mill
You receive an extra bomb at the end of every level and you cap your bombs at 9. There's no penalty to using bombs so you can use 1 or 2 per level, route with it if needed.
As far as the "Lives Remaining" bonus goes at the end of every level, it looks like 1000, then 1000 + 100, 1000+ 200 etc.
There's also the No Miss Bonus which is basically:
500,000*Amount of stages no missed in chain*Special x2 Bonus if you press "confirm" after the "success" "x2" "x3" prompt comes on screen at the end of a level.
500.000*1*2 = 1.000.000
500.000*2*2 = 2.000.000
500.000*3*2 = 3.000.000
500.000*4*2 = 4.000.000 (Gauntlet)
500.000*5*2 = 5.000.000
500.000*6*2 = 6.000.000
500.000*7*2 = 7.000.000
500.000*8*2 = 8.000.000 (TLB)
Which brings the TOTAL No Miss Chain for the whole game to a max of 36.000.000 points (literally 50% of the score, or if optimal, 42%)
So here's how it works...
Every enemy has a determined medal value, or amount of medals they can give you.
Your combo level works as a multiplier for that score so combo levels are
50 = 1x The Medal Value
250 = 2x MV
750 = 3x MV
1000 = 4x MV
Combo Multiplier Value (Combo x Medal Value, CMV from now on) plateaus at max level which means that getting combo values above 1000 in a level is extremely important in order to get the most lucrative amount of points. This value carries over from stage to stage. When it comes to medal spawns, it just looks if it's divisible by 1/5/10. This is what you refer as "making stage 2 tanks leave 4 medals instead of 2".
You have a combo timeout which will be reset everytime you either get a hit on an enemy or with a medal pickup. Combo timeout is at 80frames/steps. It resets to 0, so like 1 and 1/3 seconds.