Does those two have a similar sound signature? Would you say there's any point in getting the ts-662's if one already got the Pro80's?
In sound quality (for my ears, of course) I would put TS-662 above Pro 80's
I didn't test that while I had dt880 but I suppose isolation is pretty much the same with 2050. Something with completely open back would be better but I doubt those would not work either without lowering the sound volume a lot. Bone conduction headphones would be the answer but I'm pretty sure those sound horrible.
Sony has some headphones that might work well. Ma900 looks like it might let outside sound in. Cheaper alternative could be Sony MDR-605LP if you can find those anywhere. Those might not sound that great but maybe you could put some other drivers there. Ultimate way to solve the problem would be akg k1000 if amping is taken care of and money is not an issue :)
For what it's worth, I asked Takstar what was best between Pro 80, HD5500, and HD6000. This was their reply: