APL (Dyalog Unicode), 44 bytes

thanks @Adám for the ⍸⍣ ̄1 trick

(⊂a)∊(⍉ ̈⊢,⌽ ̈)⍣2≥∘i ̈⍳⌈/,i←⌊/↑⍳⍴a←⍸⍣ ̄1(⊢-⌊/)⍸⎕

Try it online!

APL (Dyalog Unicode), 44 bytes

thanks @Adám for the ⍸⍣ ̄1 trick

(⊂a)∊(⍉ ̈⊢,⌽ ̈)⍣2≥∘i ̈⍳⌈/,i←⌊/↑⍳⍴a←⍸⍣ ̄1(⊢-⌊/)⍸⎕

Try it online!

⍸⍣ ̄1(⊢-⌊/)⍸ trim surrounding 0s

≥∘i ̈⍳⌈/,i←⌊/↑⍳⍴a generate L-shapes

(⍉ ̈⊢,⌽ ̈)⍣2 add reflections

(⊂a)∊ test if the (trimmed) input is among them