You may wish to consider, assuming everything stays the same in terms of the US being an amber country, that actually it wouldn’t make much difference to your costs if you stayed overnight in London and flew to Greece the next day (to minimise the risk of missing the ATH flight on separate tickets).

If remaining in the UK for less time than would trigger the two day PCR test (the day of arrival counting as zero), you would not have to pay for any tests beyond the normal pre-flight one. So you could cross the border, collect your luggage, travel directly to a hotel (where you’d have to self-isolate, so you’d be stuck there) and then travel directly back to the airport for your flight the next day.

The alternative is to leave a lot of time for the connection, taking a flight to ATH many hours later on the same day, but there is still the potential for very, very long delays at the border - plus BA is cancelling lots of flights right now, so you might end up having to change arrangements anyway. There’s certainly a degree of stress in that arrangement at the moment.

Going hand baggage only would mean you didn’t need to cross the border - a transfer desk at T5 should be able to process you if you couldn’t do OLCI because of required document checks - so you’d only be judging the risk of transferring on separate tickets. If that’s on BA ticket stock, you’d be covered by their Book with Confidence if it was obvious something was going badly wrong in terms of delay, but you’d still potentially be on the hook for fare difference (although that’s still able to be mitigated by choosing at fare with free same day change).