I'd would consider another railway to use that temporary until Euston International is built, HS 2. The track is there from Old Oak, just needs a bit of infrasture built to connect up the new Station to the West London Lines.
Are you saying that international services could stay above ground across South London (while using HS1 tunnels for getting across Kent) - as they did towards the end of Waterloo International times - but then [one day, after using Waterloo again for now] go "straight on" after Brixton (rather than "turning right" over the link into Waterloo built for the international service)? And then on, via the maze of lines east of Clapham Junction, to the West London Line and up towards OOC? (So far so perfectly possible, with a bit of gauge clearance, even if slow.) And
then, somehow, getting deep underground to join tunnels [which might never exist...] to terminate at Euston? It's a bit of crayoning I hadn't seen before ... though perhaps no less possible, in principle, than suggestions to get trains from the tunnel into St P on to Euston or elsewhere.
Or perhaps the
least impossible option is a link from the tunnel mouth at St P, via the NLL, to the
above ground (being expanded) OOC complex to terminate there? That could provide an interchange connection with HS2 (if it ever gets that far south), and/or - in principle - a route for international trains to go north or west on existing main lines. Though this doesn't improve international services' resilience in terms of having an alternative to the HS1 tunnel under the Thames and east London, but it does provide extra terminating capacity and extra interchange options.
I hadn't realised crayons were such fun.
However, Stratford does have a huge concourse which is empty even at peak times which could surely be repurposed for additional space?
Yes - it does seem a bit obvious that using Stratford as an extra international terminus at the London end is the most feasible (least unfeasible?), if places like Ashford are thought to be too far out to be a desired destination for many. Though of course an Ashford
stop (even if it isn't the terminus) - particularly on anything running other than to St P (as per crayons above) - does spread the terminal load at least a bit, as well as providing additional connections around the soouth-east; and tickets to/from Ashford could be cheaper (and/or include "local" - ie SE England - onward journeys in the price).