Sorry mate I don't believe your analysis is foolproof.
The actual Fire that the detectors detected will most likely damage the detectors won't it?
I would expect that the test for that Engine would not pass.
In this case you may be led down the garden path to land at an Airfield you don't really want to be at.
The Airbus ECAM has a RED LAND ASAP with a Fire and that about covers it....
There are other things you will do to ascertain the state of the Fire and :--
LAND ASAP.
I still say that both Airbus and Boeing would have considered this possibility ( everything they do is with litigation in mind and ass protecting ) and decided against it for very good reasons not least being it may not be a reliable check of the system or indicate the level of damage to the Engine.
Oh and yes most definitely there is a time and a place to vary procedures as required, as has been shown many times
( as indeed Airbus and Boeing advise )