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Python 2, 591 555 545 527 525 496 436 351 334 333 303 bytes
s=input()
w=len(s[0])
h=len(s)
V=max(0,w/2-h)
H=max(0,h/2-w)
p=[[' ']*w]*V
q=[' ']*H
s=[q+k+q for k in p+s+p]
d,c=' -=',' |"'
exec"c,d,V,H,w,h=d,c,H,V,h,w;s=map(list,zip(*s))[::-1]\nfor j in range(h-4):q=s[V+j+2];q[H]=c[q[H]==c[2]];r=...