  It was recently shown by Gaidashev and Yampolsky that appropriately defined
renormalizations of a sufficiently dissipative golden-mean semi-Siegel H\'enon
map converge super-exponentially fast to a one-dimensional renormalization
fixed point. In this paper, we show that the asymptotic two-dimensional form of
these renormalizations is universal, and is parameterized by the average
Jacobian. This is similar to the limit behavior of period-doubling
renormalization in the H\'enon family considered by de Carvalho, Lyubich and
Martens. As an application of our result, we prove that the boundary of the
golden-mean Siegel disk of a dissipative H\'enon map is non-rigid.
