Wolfram Language (Mathematica), 212 170 166 164 159 157 155 bytes

A_~J~B_=Fold[Switch[{a,b}=#;#2,3,Echo@a;#,4,#+Min[a,B-b]z,5|6,{(#2-5)A,b},7,Echo@b;#,8,#-Min[b,A-a]z,_,{a,(#2-9)B}]&,z={-1,1};0z,ToCharacterCode@#~Mod~12]&

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Wolfram Language (Mathematica), 212 170 166 164 159 157 155 153 bytes

A_~J~B_=Fold[Switch[{a,b}=#;#2,3,Echo@a;#,4,#+Min[a,B-b]z,5|6,{#2A-5A,b},7,Echo@b;#,8,#-Min[b,A-a]z,_,{a,#2B-9B}]&,z={-1,1};0z,ToCharacterCode@#~Mod~12]&

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Wolfram Language (Mathematica), 212 170 166 164 159 157 bytes

A_~J~B_=Fold[Switch[{a,b}=#;#2,3,Echo@a;#,4,#+Min[a,B-b]z,5,{0,b},6,{A,b},7,Echo@b;#,8,#-Min[b,A-a]z,9,{a,0},_,{a,B}]&,z={-1,1};0z,ToCharacterCode@#~Mod~12]&

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The program is a big Switch statement folded over the character codes (modulo 12) of the program, step-wise updating the contents of the buckets. Dispatching the Switch takes a shortcut by defaulting to "F", as the spec says that there are no characters to be expected other than "fFeEpPoO".

Wolfram Language (Mathematica), 212 170 166 164 159 157 155 bytes

A_~J~B_=Fold[Switch[{a,b}=#;#2,3,Echo@a;#,4,#+Min[a,B-b]z,5|6,{(#2-5)A,b},7,Echo@b;#,8,#-Min[b,A-a]z,_,{a,(#2-9)B}]&,z={-1,1};0z,ToCharacterCode@#~Mod~12]&

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The program is a big Switch statement folded over the character codes (modulo 12) of the program, step-wise updating the contents of the buckets. Dispatching the Switch takes a shortcut by defaulting to E|F (9|10), as the spec says that there are no characters to be expected other than "fFeEpPoO".

Wolfram Language (Mathematica), 212 170 166 164 159 bytes

A_~J~B_=Fold[Switch[{a,b}=#;#2,"f",{A,b},"F",{a,B},"e",{0,b},"E",{a,0},"p",#+Min[a,B-b]z,"P",#-Min[b,A-a]z,"o",Echo@a;#,_,Echo@b;#]&,z={-1,1};0z,Characters@#]&

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The program is a big Switch statement folded over the characters of the program, step-wise updating the contents of the buckets. Dispatching the Switch takes a shortcut by defaulting to "O", as the spec says that there are no characters to be expected other than "fFeEpPoO".

Wolfram Language (Mathematica), 212 170 166 164 159 157 bytes

A_~J~B_=Fold[Switch[{a,b}=#;#2,3,Echo@a;#,4,#+Min[a,B-b]z,5,{0,b},6,{A,b},7,Echo@b;#,8,#-Min[b,A-a]z,9,{a,0},_,{a,B}]&,z={-1,1};0z,ToCharacterCode@#~Mod~12]&

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The program is a big Switch statement folded over the character codes (modulo 12) of the program, step-wise updating the contents of the buckets. Dispatching the Switch takes a shortcut by defaulting to "F", as the spec says that there are no characters to be expected other than "fFeEpPoO".