anywhere you are doing this....

aSpriteInit(&demoSpr,&bmary_spr,53,16 + ffbg_a.palInfo->count + ffbg_b.palInfo->count + ffbg_c.palInfo->count,x,y,0,FLIP_NONE,AS_FLAGS_DEFAULT);
palJobPut(16 + ffbg_a.palInfo->count + ffbg_b.palInfo->count + ffbg_c.palInfo->count,bmary_spr.palInfo->count,&bmary_spr.palInfo->data);

Please stop.....

If I want Blue Mary to use pal slot 25 the code would like this...

aSpriteInit(&demoSpr,&bmary_spr,53,25,x,y,0,FLIP_NONE,AS_FLAGS_DEFAULT);
palJobPut(25,bmary_spr.palInfo->count,&bmary_spr.palInfo->data);

Adding this to that and that to this is clouding your issue. Make simple definitions for your scrollers,sprites and pictures....You can get elaborate after you get the basics down....

EX: I would start my pal slots at 16 and above because 0-15 is used for the fix layer aka your text
With that in mind if your background has 5 pals and you Init your scroller at pal slot 16 then Blue Mary would start at 21 because she should not overwrite your background palette.
The same principal is true when allocating sprites.

Your images depict palette slots that are being used by another graphic causing the ugly colours.

EX: All I would start with is 1 background, 1 Blue Mary and 1 Cigar Man.....
I would not include extra scrollers to complicate matters.

Remember simple Inits so you can clearly understand what the function's need. You will need to be very well versed in these function's.