  Context: Our previous models of a giant planet migrating through an inner
protoplanet/planetesimal disk find that the giant shepherds a portion of the
material it encounters into interior orbits, whilst scattering the rest into
external orbits. Scattering tends to dominate, leaving behind abundant material
that can accrete into terrestrial planets. Aims: We add to the possible realism
of our model by simulating type I migration forces which cause an inward drift,
and strong eccentricity and inclination damping of protoplanetary bodies. This
extra dissipation might be expected to enhance shepherding at the expense of
scattering, possibly modifying our previous conclusions. Methods: We employ an
N-body code that is linked to a viscous gas disk algorithm capable of
simulating: gas accretion onto the central star; gap formation in the vicinity
of the giant planet; type II migration of the giant planet; type I migration of
protoplanets; and the effect of gas drag on planetesimals. We use the code to
re-run three scenarios from a previous work where type I migration was not
included. Results: The additional dissipation introduced by type I migration
enhances the inward shepherding of material but does not severely reduce
scattering. We find that > 50% of the solids disk material still survives the
migration in scattered exterior orbits: most of it well placed to complete
terrestrial planet formation at < 3 AU. The shepherded portion of the disk
accretes into hot-Earths, which survive in interior orbits for the duration of
our simulations. Conclusions: Water-rich terrestrial planets can form in the
habitable zones of hot-Jupiter systems and hot-Earths and hot-Neptunes may also
be present. These systems should be targets of future planet search missions.
