I think more people would have responded if you had used the word "casing" to describe what you want to install. I've coped more than my fair share of miter joints, but I have yet to hear of installing "coping" where one would normally install door "casing".
I can't see any good way around this problem either; except perhaps to install stained and varnished wood panels on each side and the top of the doorway to match the casing. That would allow you to run those wood boards to the floor on both sides of the door way, along with the casing, and therefore have your baseboards and shoe moldings stop at the casing.
That would prolly look a bit nicer, but it would make for a narrower doorway, AND only you know how thick those boards need to be to cover the gap currently being covered by the baseboard and shoe molding.
I'm presuming you have plaster or drywall in the entranceway now, rather than a wooden jamb. By rights, if you had a wooden door jamb in that entranceway, whomever installed that wood flooring really should have undercut the wooden jamb on each side of the entrance way to allow the flooring to go under the wooden jam. But, if the sides of that entranceway were plaster or drywall, their only option was to install baseboard and shoe molding instead. If what you have now is drywall, I'd be inclined to pull it off, put up 3/4 inch thick stained and varnised clear fir to match your casing, and solve the problem that way, but that all depends on your level of skill and experience.
ALSO, the bottom line is that most visitors to your home won't notice what you've done there regardless of what you do, so don't be concerned about it looking "odd". Things only look odd if they're different than normal _and_they_get_noticed_, and in most cases, it's that second element that's absent. That's great if you're sensitibe about it, but it's frustrating when you know you've done a top notch job, and all people seem to compliment you on is your choice of paint colours.
The easiest thing to do would be to either cope your casings to fit nicely around the top of the baseboards, or deep six the idea of installing that casing in the first place, and just leave what you have the way it is. But, nobody's going to laugh out loud if you stop the casing at the baseboard. It'll look "different" out of necessity, not because you didn't know WTF you were doing.
PS: Actually, I think the word "coping" simply means to cut along a curved line as opposed to a straight line. Coping saws, for example, are designed to cut along a curved line in any wood, not just wood moldings.
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