Some thoughts
1) The CDR or the seal between it and the valley pan could be your issue. Perhaps it is not working correctly. It is a maintenance item. These have been reported for causing head gasket failure when not working.
2) Many have experience little holes in the top of their valley pan, so yes it can leak too.
3) A valve cover gasket is perhaps leaking onto the valley pan. Then via the valley pan drain onto the tranny and starter.
4) Check your oil pressure sensor, it is on the rear of the engine above the tranny.
5) Potentially a rear main seal.
If you lost quarts over 250mi my guess is
1) The oil pressure sensor, leaks bad when driving and rpms are up. Thus why when off or at idle you cannot see it leaking.
2) You have bad blowby or a clogged CDR. When rpms are up it is pushing oil out the cdr, burning some and perhaps some leaks onto the valley pan.
Guessing here but that is a lot of oil disappearing. A small leak would not let 2 or more quarts leak out in 250 miles. So likely it is a big leak, blowby pushing it out (Perhaps by a stuck cdr.), or something under oil pressure like your pressure sensor.