  Crystal calorimeters have a long history of pushing the frontier on
high-resolution electromagnetic (EM) calorimetry. We explore in this paper
major innovations in collider detector performance that can be achieved with
crystal calorimetry when longitudinal segmentation and dual-readout
capabilities are combined with a new high EM resolution approach to PFA in
multi-jet events, such as $e^+e^+\rightarrow HZ$ events in all-hadronic
final-states at Higgs factories. We demonstrate a new technique for
pre-processing $\pi^0$ momenta through combinatoric di-photon pairing in
advance of applying jet algorithms. This procedure significantly reduces
$\pi^0$ photon splitting across jets in multi-jet events. The correct
photon-to-jet assignment efficiency improves by a factor of 3 with a
$3\%/\sqrt{E}$ EM resolution. In addition, the technique of bremsstrahlung
photon recovery significantly improves electron momentum measurements. A high
EM resolution calorimeter increases the Z boson recoil mass resolution in
Higgstrahlung events for decays into electron pairs to 80% of that for muon
pairs. We present the design and optimization of a highly segmented crystal
detector concept that achieves the required energy resolution, and a time
resolution better than 30 ps providing exceptional particle identification
capabilities. We demonstrate that, contrary to previous detector designs that
suffered from large neutral hadron resolution degradation from one interaction
length of crystals in front of a sampling hadron calorimeter, the
implementation of dual-readout on crystals permits to achieve a resolution
better than $30\%/\sqrt{E}\oplus 2\%$ for neutral hadrons. Our studies find
that the integration of crystal calorimetry into future Higgs factory collider
detectors can open new perspectives by yielding the highest level of combined
EM and neutral hadron resolution in the PFA paradigm.
