When you said Heathrow Express to Piccadilly that was probably a typo for Paddington- which is where the Heathrow Express goes to.
I guess your Option 2 would mean Elizabeth Line to Stratford International, then the High Speed train from there. I wonder why that route doesn't usually come up in the journey planners, which always suggest St Pancras- probably because that will be slower than St Pancras. Elizabeth Line trains from Heathrow don't go direct to Stratford (for Shenfield) from the May timetable change- they all go to Abbey Wood- so you would have to change somewhere in the Central area east of Paddington- the planners say Whitechapel, but anywhere would do. So that sounds a slightly odd route, if valid.
South Eastern say you can buy advance tickets for St Pancras to Canterbury up to 2359 the previous night. At 2300 I can still see advance tickets for tomorrow morning at £21.20, so that seems to be true. That suggests that, as soon as you know what time your plane is actually taking off (as opposed to it's ticketed time) you could take a reasonable punt and buy an advance ticket on your phone from St Pancras for 3 or 4 hours after landing.
To me personally the tube route all the way from Heathrow to King's Cross St Pancras is what I would choose, rather than any other (and there are several, which various people have suggested, I think we have 5 or 6 variations now from different people) requiring a change. The Tube route is only about 10 minutes slower than any of the routes involving the Elizabeth line.