Can I use the secret part of a asymmetric encryption keypair as a symmetric encryption key?
The HMAC calculation is used as a KDF here. So 3 keys are derived.

Let's start with the statement "In practice, if you know one, you'll know the other.". This is incorrect. The KDF construction uses a one way function so that you cannot get to the input keying material (or seed) s. This means that if an adversary gets hold of the symmetric key c that you cannot calculate either s and therefore e or d.

There is another more theoretical problem in the sense that using d both for HMAC as for "symmetric secret key" then you're using the same value for multiple algorithms, breaking their security claim. It might be that there is some mathematical algorithm that makes the value of s vulnerable. From a practical perspective that's highly unlikely as a HMAC with a known string will not be a structure that can be abused for this kind of attack - but I think it is worth mentioning anyway. For instance, an auditor may ask nasty questions about it.

From a more practical point there may be an issue when it comes to side channel attacks. If these can be combined then there may be a practical issue when the keys are not separated (this is of course a blatant copy of the comment by fgrieu below).

And that's about it; the reason to separate the keys is key separation itself. If you want to break that rule then that's your decision, but it is certainly not considered good cryptographic practice. I'd only do such tricks if there is no other way.