I was under the impression that the old work by Chung, Kibble, Kulish+Faddeev,QED's infra-red problem is mainly related to the asymptotic space of states not being a Fock space. Essentially because photons are massless, all electrons pick up a soft photon cloud. These electron + cloud and photon + cloud states are the appropriate in/out states. However getting enough information on these states to show a unitary S-matrix exists between them is very difficult. So QED's infrared problem is a massless force carrier problem which makes a treatment of the S-matrix difficult.
and more recently Lavelle+McMullan+et al, had already found the appropriate
asymptotic states -- in which asymptotic electrons are accompanied by a Coulomb
and radiation field -- and that this solves the QED IR problems to all orders.
Kibble constructs a very large nonseparable space, but Kulish+Faddeev just
concentrate on the asymptotic spaces, deriving an S-matrix that maps
between them. (This is probably only at the level of rigor of theoretical physics,
borrowing Arnold's phrase. :-)
In these treatments of IR, they don't bother to dress the asymptotic photons since
no residual part of the interaction remains at light-like infinity. Could you give some
details/references about the "photon + cloud" you mentioned, as relevant in this