It's a shame the former HSS inner harbour, much closer to the train station, cannot be used since it was abandoned years ago.
It's not unusable, it just doesn't have the required linkspan. The Stena HSS used highly custom infrastructure, including linkspans, and so when the service ended, this was torn out. If someone was to put a linkspan in there, nothing would stop it being used again. Holyhead has the physical capability, it's just that neither Stena (the owner of the port) nor Irish Ferries want to pay for it.
Can't they run it from Liverpool using the SteamPacket terminal?
Economically, no. It would never work: the selling point of the Swift is the fastest crossing of the Irish Sea, not a lengthy run to Liverpool.
Not sure it has the required capacity and staffing for UK customs and border control inbound from the EU.
That's not a major issue in itself, as there's no need for large scale UK immigration facilities, and commercial traffic could simply be banned if customs clearance is an issue. Alternatively, it could be perfectly possible to pre-clear vehicles when they're still in Ireland, directing them to the conventional ferries if customs clearance is required in the UK.