Whatever way you look at it, there isn't anywhere which can be used as a temporary terminus at short notice. As Finsbury Park proved a decade ago, there isn't anywhere with the physical capicity.
This whole question illustrates why the Railway Lands at Old Oak Common should have been used to create a proper interchange station with access from the Great Western, the Chiltern and the West Coast. As well as HS2, the EL, and the Overground routes. It could have acted as a temporary terminus for Euston, Marylebone and Paddington as required as each was upgraded.
As that land is no longer available, I would propose building a cheap four-platform open-air station on what used to be the Willesden Freightliner sidings and is now an HS2 logistics yard. With access from WCML fasts. Then build a high-level pedestrian walkway across the road to the DC line platforms at Willesden Junction.
Convert the DC lines to Bakerloo only, at least as far out as Harrow & Wealdstone, and ideally all the way to Watford. Upgrade the Bakerloo to 24 or 32 tph; whatever is needed to handle the passenger flow, with a second terminating platform between platforms 1 and 3 at Willesden, so that 12tph start from Willesden.
Keep an Overground Shuttle between Euston and Queens Park where possible but divert it onto the North London line during Euston redevelopment works. More than half the passengers on Overground services get off at Queens Park anyway, to change onto the Bakerloo, so making the DC lines Bakerloo only would reduce the total number who change there.
With 400m platforms at the new station at Willesden, you could use surplus HS2 stock already on order to carry 1100 passengers per path and fill them with the price-senstive customer segment who currently have to wait around at Euston until 7pm to get home. With 540m platforms, you could double up 11-car Pendolinos, splitting and joining at Crewe, or Rugby. Wherever you can extend platforms. Four platforms at Willesden could replace eight platforms at Euston.
Keep some Avanti services through to Euston, to serve the time-sensitive premium price market. But they could use just half the station while the rest was being rebuilt.
And build a 750 metre long overhead pedestrian walkway to Old Oak Common too, so there is a possible diversion route available if the Bakerloo line is ever closed. Or use the HS2 logistics tunnel if that is available.