How would I convert committed coordinates $x$ and $y$ to a commitment of the EC point without revealing the point (in Zero Knowledge) or vice versa? I am working in the secp256k1 elliptical curve, though I suspect this would apply to any elliptical curve.  I have a Pedersen Commitment of the $x$ and $y$ coordinates in some discrete log scheme with generators $g$ and $h$. The point described by $x$ and $y$ is equal to $G^n$, where $G$ a public generator and $n$ is a secret (using exponentiation to represent point scalar multiplication on elliptic curves). Is there a method to get from the $g^x h^{r_1}$ and $g^y  h^{r_2}$ to $G^n H^{r_3}$, where $H$ is a second generator in the curve and all $r$ values are secret random numbers, using Zero Knowledge Proofs where needed?  A method in the other direction, going from the commitment of $n$ to a commitment of the two coordinates $x$ and $y$ would also be applicable.  I haven't been able to find such a proof in my research and I have not been able to think about how to create one.  

My goal is to design a Zero Knowledge Proof of Knowledge of the private key associated with a public key which has been hashed (using the Bitcoin address hash) in such a way that the only public information is the environments (generators, settings, etc) and the result of the hash function, as well as all associated functions like the Bitcoin Hash. This proof can be used to prove ownership of a non-spending Bitcoin account without revealing the public key. If someone has done this, then I guess the question is moot and I will reference an applicable paper instead of designing it myself, thus a link to any such paper would also be an acceptable answer to this question. Unfortunately, I have not seen such a paper myself in my research.

EDIT: 

I should also note that before the commitments of the coordinates were in the form $g^x h^{r_1}$ and $g^y h^{r_2}$, they were two lists of bitwise commitments that were homomorphically combined to become $g^x h^{r_1}$ and $g^y h^{r_2}$.  I did not lose those commitments, so they are available.  It was probably a mistake to suggest combining them, as it could introduce problems in performing operations on them due to differing orders between groups.
It's quite useful that you included yuor actual goal in the question, to avoid the XY problem.


  My goal is to design a Zero Knowledge Proof of Knowledge of the private key associated with a public key which has been hashed (using the Bitcoin address hash) in such a way that the only public information is the environments (generators, settings, etc) and the result of the hash function, as well as all associated functions like the Bitcoin Hash.


If we assume that pulic parameters are known by everyone, you only give the verifier a single piece of information: The hash-value of the public key. And here it is quite irrelevant what kind of public key is used - you need a ZK proof for a preimage under the according hash function.

I am not sure what you mean with "all associated functions like the Bitcoin Hash". But the goal here seems to be keeping the identity of the Bitcoin account secret, so I guess that additional information does not reveal the public key either.


  This proof can be used to prove ownership of a non-spending Bitcoin account without revealing the public key.


Actually, this is probably wrong. The reason for this is, that knowledge of a preimage under a hash function does not guarantee that the preimage is actually a valid Bitcoin account. For that you would need a different ZK proof, in which the verifier actually needs the according public key.

In the setting of Bitcoins, I think your agoal is not achievable. What you actually would need is a proof for membership of a group, e.g. the group of owners of valid accounts, and I can imagine that being possible - if the system is designed that way. This would be similar to group signatures, etc. But without an according setup, I don't see any way to achieve your goal. 



Regarding your idea with the commitments and the EC public key:

You have two Pedersen commitments $a = g^xh^{r_1}, b = g^yh^{r_2}$ and then $c = G^nH^{r_3}$, which is like a Pedersen commitment but not in a prime order group but an elliptic curve.

Now, regardless of what $x$ and $y$ actually are, $a$ and $b$ could potentially be any element of the group, because the Pedersen commitments are perfectly hiding. So maybe you can generate $G^nH^{r_3}$ somehow from $a$ and $b$, but that will definately reveal $n$ itself and it has actually no relation to $x$ or $y$.