80mins is enough time to make the connection with the bags checked through
I think you do not have enough time to collect and recheck your bags at lhr
your bags will be tagged through to fco. if you ask for the bags to be short checked to lhr you will probably struggle. this has been clamped down on to prevent people not completing their journey. to get the bags short checked you would need an overnight or a change of airports.
if the bag is through checked and you miss the connection and end up overnight in heathrow then you can ask for your bag to be retrieved. your bag will not go to fco without you on the plane