I'd take the Eurostar, but maybe add some buffer by booking the train before the 'ideal' one, just to give yourself some margin in case of a delay or cancellation, you can enjoy extra time in the LHR lounge

At holiday times, queues at Gare du Nord can be long, I'd have thought an hour would be enough on a Saturday, though if EES has slowed things it might be better to play safe. Tbh I use the business lane, the normal ones always seem to flow pretty well, but I've only done a couple of trips post-EES and not at busy times.

As mentioned above, for many months the Piccadilly line has had closures at weekends for engineering work, so if you plan on using it, check the status in advance, you can do that here https://tfl.gov.uk/tube-dlr-overgrou...us/#piccadilly

Unless you've got heavy baggage, from stepping off the Eurostar to reaching the Piccadilly line platform would take me about ten minutes, it's the least-effort transfer option. If you've got baggage, you might prefer getting a taxi from St Pancras to Paddington, and get the train from there.