I'm thinking,neither. . .There has to be something with The Jumping Man going down the stairs of the "connivence store"  when Coop and Gerard go up

That's a good point. Hadn't even considered the implications of that......

Looking forward to many years of theorizing......

Don't have a great answer. He seems a reunified version of Dale and Mr. C. The former is never perfectly good and the latter never perfectly bad. Both have his psyche and drive and for the same goal though their ultimate ends may differ. I think wow bob wow is on to something that jumping man got to Jeffries first and set him up to fail. Note the reversal of the infinity sign as he's locating. So probably the scene of Laura disappearing in the woods and Laura being ripped out of the red room are simultaneous, possibly on a loop. Richard is possibly Dale in a Tulpa world doomed to continually perpetrate horror on Laura in the vain attempt to save her. Or something like that. Will take years to make sense of it. 

He is Cooper there. Richard is simply his name in the fake Carrie Page Universe. Cooper seems changed at that point because he had just joined with his body that had returned to him in the waiting room after BOB is beaten at the sheriff station. He now has the memories of what Mr. C did using his body. I am sure they aren't pleasant.  So, Mr. C is now part of him. Similar to Leland waking up at the end. 

I can't get onboard with the idea that "Richard" is partly (or a version of) Mr. C. His moral compass still seems to be set correctly; he's just more ruthless than "our" Coop would be about enforcing it.

I've posted about this at greater length elsewhere, but the short version is I think he's literally "Cooper in a parallel universe." That is, Cooper in different circumstances - perhaps a Cooper who's had a harder life or a less loving family or a neglected childhood. (Not that we know any of that about Cooper anyway - just suggesting things that could make the "same" person turn out harder and colder.) He's Coop without the warmth and spirit... which to me is actually eerier than Mr. C, because he's almost right, yet unmistakably wrong.

It reminds me of the "uncanny valley" hypothesis, which says the creepiest robots are the ones that seem almost human. Same deal.

Could Mr. C actually be an alternative Cooper that became so spiritually corroded that he turned evil? Thus, Real Cooper needed to pause his mission to save Laura in order to destroy this alternative version of himself.

I already posted this on another thread, anyway:

Before being called in by someone looking like Coop, Diane sees her double. In the motel she is Diane, but gets increasingly unsure about Coop. In another motel, Coop wakes up only to discover he's been left by a Diane-looking Linda who calls him Richard. He probably took that woman away from the first motel because he mistook her for Diane. In other words: Diane is coupled with Richard, Coop with Linda, but only Diane gets it (too late, when already having sex with him). The doppelganger rape is mutuated (sort of) and she never makes love to the "real and only one".
Moreover, Coop is possessed again. But, unlike Mr C, who got rid of his good half in some mysterious way (probably connected to his tulpa engineering) he's back again in the situation of the closing of the old series: like Leland, the bad personality takes momentarily over but the good one doesn't remember about it. He was possessed by returning to the Black Lodge in the past. When he comes out of Glastonbury Grove, he's already possessed. Bob has every convenience in staying "in stealth mode" and letting him get Laura first and Mother second.
Moreover, this is all Laura's dream and the negative force of Mother is wake world destroying everything we knew. Bob, finding Mother, destroys the (dream) world, revealing himself as a life-force, however demonically phallically so.