There is indeed a similar re-check process in T7 as there is in MIA, and it's the norm in the USA, I cannot think of an airport with international flights which doesn't have them (SLC maybe?). It should in theory then end up in T8 and then your flight.

However! While the rule generally is a maximum of 24 hours in transit airports, in the USA it's often 12 hours. Furthermore if anything makes your bag stick out from the general mass, there is a chance of things going wrong. And most baggage transits in the USA are short timed domestic hops. If it gets left off, it will get to you within a day or two, but if you have an overnight stop I suggest you take it with you, or pack so as to be OK for a few days without it. Or go HBO (hand baggage only)!!!

Some people prefer to take their bags to T8 themselves, on the "one less thing to go wrong" basis. Though the two terminals are next door to each other, there is a highway between the two buildings.

There is a luggage storage facility in T8, and also at places like Penn Station.