I'll start with LHR being on my wife and I's 'no fly list'. We find it a disaster as an airport even without a situation such as you describe. No doubt there will be lots of posters who disagree.

Second, I will remind you that Brexit may affect your plans as it comes into affect on March 30 and at the least, may easily affect lineups at Customs/Immigration considerably. No one can tell you what affect it is going to have. What exists today will not exist in June.

If you do not intend to spend any time in the UK, why are you not flying direct to Athens? Or through any European airport other than in the UK. That would eliminate all of this. My guess is that you found a cheap flight from London to Corfu and are basing everything on that one factor. I understand a wish to spend less but sometimes other costs (time, hassle) can be higher than the $ costs.

If I wanted to fly from Denver to Corfu, I would be flying Emirates direct from Newark to Athens with the necessary connections at both ends. Or I might look at Aer Lingus from Chicago to Dublin and connections. They fly Dublin to Corfu.