I think that it a very good idea.
But I think that you will have a problem during check-in.
Because if the time between the outward and return date for the EK flight is more then 30 days EK will need to see a visa for Thailand in your passport.
EK is under the impression that you stay the whole time in Thailand and most countries only get a 30 days visa exemption stamp for Thailand at Bangkok airport.
So according to EK you can’t stay legally in Thailand for the whole time.
Try to get a double entry tourist visa for Thailand with which you can stay 2 x 60 days in Thailand and inform EK during check-in that with this visa you can stay in Thailand for 120 days with only a visa run after the first 60 days. ( the 120 days can be extended with 2 x 30 days at any immigration office inside Thailand )
As EK doesn’t know that you leave the country with BA you have to give them a explanation.