J, ⁸⁰ 69 bytes

[:+/@,1 2 3*((,.@1;];[:,/[:,./"3#"{~)#:2 7 2)4 :'y(x-:x&*);._3~$x'&><

Try it online!

J, ^{80 69} 60 bytes

[:+/@,[,2 3*((;[:,./^:2#"{~)#:2 7 2)4 :'y(x-:x&*);._3~$x'&><

Try it online!

^{-9 thanks to xash}

J, ^{80 65} 61 bytes

1#.[:,1 2 3*#:@2 1 2*(3,:1,:3 3)((]-:*)#:@2 7 2);._3"2^:(<3)]

Try it online!

^{-15 thanks to inspiration I got after reading Neil's approach}

There is currently a small bug in the 61 byte version. I'll fix it tomorrow -- meanwhile consider the other answer official.

original approach, 80 bytes

[:+/@,1 2 3*((,.@1;];[:,/[:,./"3#"{~)#:2 7 2)([-:*/@,:)&>/[:,(,.~3^/i.3)<;._3"$]

Try it online!

J, ⁸⁰ 69 bytes

[:+/@,1 2 3*((,.@1;];[:,/[:,./"3#"{~)#:2 7 2)4 :'y(x-:x&*);._3~$x'&><

Try it online!

J, ^{80 65} 61 bytes

1#.[:,1 2 3*#:@2 1 2*(3,:1,:3 3)((]-:*)#:@2 7 2);._3"2^:(<3)]

Try it online!

^{-15 thanks to inspiration I got after reading Neil's approach}

original approach, 80 bytes

[:+/@,1 2 3*((,.@1;];[:,/[:,./"3#"{~)#:2 7 2)([-:*/@,:)&>/[:,(,.~3^/i.3)<;._3"$]

Try it online!

J, ^{80 65} 61 bytes

1#.[:,1 2 3*#:@2 1 2*(3,:1,:3 3)((]-:*)#:@2 7 2);._3"2^:(<3)]

Try it online!

^{-15 thanks to inspiration I got after reading Neil's approach}

There is currently a small bug in the 61 byte version. I'll fix it tomorrow -- meanwhile consider the other answer official.

original approach, 80 bytes

[:+/@,1 2 3*((,.@1;];[:,/[:,./"3#"{~)#:2 7 2)([-:*/@,:)&>/[:,(,.~3^/i.3)<;._3"$]

Try it online!