  We present a rigorous analysis of the transient evolution of nearly circular
bilayer interfaces evolving under the thin interface limit, $\varepsilon\ll1$,
of the mass preserving $L^2$-gradient flow of the strong scaling of the
functionalized Cahn-Hilliard equation. For a domain $\Omega\subset{\mathbb
R}^2$ we construct a bilayer manifold with boundary comprised of
quasi-equilibrium of the flow and a projection onto the manifold that
associates functions $u$ in an $H^2$ tubular neighborhood of the manifold with
an interface $\Gamma$ embedded in $\Omega$. These interfaces, and hence the
bilayer manifold, are parameterized by a finite but asymptotically large number
of degrees of freedom. The manifold contains a unique, up to translation and
mass constraint, equilibrium of the gradient flow whose projected interface is
circular up to exponentially small corrections. The thin tubular neighborhood
is forward invariant under the flow with orbits that ultimately converge to the
equilibrium. Projections of these orbits yield an interfacial evolution
equivalent at leading order to the regularized curve-lengthening motion
characterized by normal motion {\sl against} mean curvature, regularized by a
higher order Willmore expression. The curve lengthening is driven by absorption
of excess mass from the regions of $\Omega$ away from the interface,
generically leading to nontrivial dynamics that are ill-posed in the
$\varepsilon\to0$ limit.
