Python 2, 131 131 130 bytes
x=input()
n=len(x)
s=" "
for v in[" "*2*n+"_"*in[s*2*n+"_"*(2+len(x[0]))]+[" "*i+"\\"+" "*]+[s*i+"\\"+s*2*(n+~i)+"/"+" "*"+s*-~i+r for i,r in enumerate(x)]:print v[n/2:]
A full program taking a list of lines as input with the rectangular-only allowance (actually that the first line is one of the longest).