Question

Hello Rabbi!
According to the Beit Yosef, one must wait 6 hours between meat and dairy, but there is no need to wait at all between a meat dish and dairy (at most, rinsing is required).
According to the Rema, one must wait an hour ("and the common custom in these countries is to wait one hour after eating meat, and afterward eat cheese"), though he recommends 6 hours, and one should also be stringent and wait even between a meat dish and cheese (unlike the Beit Yosef).
It follows that for Sephardim, immediately after drinking chicken soup (without the chicken itself!), it is permitted to drink milk.
My question is whether Ashkenazim who customarily wait 6 hours also need to wait 6 hours between a meat dish and cheese, or perhaps they are not stringent to that extent—that is, they do not add one stringency on top of another, and even though between actual meat and cheese they wait 6 hours, between a meat dish and cheese, where waiting itself is already a stringency, perhaps they should wait only the one hour of the common custom?
 
In short: is it permitted to drink coffee after a meat dish, without the meat itself?