Block-repetition identities for alternating-sign-matrix numbers

Let $A_n:=\alpha(n;1,2,\ldots,n)$, where $\alpha$ is the generalized monotone-triangle enumeration. Let $n\geq1$, let $i$ range over $0,\ldots,n$, and define

$$W_{n,i}=\alpha(2n+1;i,2,\ldots,n+1,1,2,\ldots,n),\qquad i=1,\ldots,3n+2.$$

Block-repetition conjecture. The identities

$$A_n=\alpha(n+i;1,2,\ldots,i,1,2,\ldots,n),$$

for $i=0,\ldots,n$, and

$$A_n=(-1)^n\alpha(2n+1;1,2,\ldots,n+1,1,2,\ldots,n)$$

should hold, and the numbers $W_{n,i}$ should satisfy

$$W_{n,i}=W_{n,3n+3-i}.$$

These identities were conjectured using mathematical computation, and the source presents bijective proofs as an open direction.