Storing RSA private key
I am currently hoping to find an answer to a similar problem, but maybe I can share some ideas. I would say that your problem is more standard than mine, and therefore it has the benefit that the existent options are relatively standard. However, my own question made me realize that key storage is an information security problem, as opposed to a cryptographic problem. With this, I mean that there is no provable best approach, but there are techniques and good practices that could help to mitigate risks, given some threat model.

Said threat model is, in fact, the most critical aspect to determine what is relevant. There are some approaches in terms of good practices, but they should be considered more as suggestions than as a checklist or a perfect answer.

One aspect that seems to be relatively agreed upon is that the encryption should happen within an environment separated from the normal processor (i.e. TPM, HSM, smart cards). I haven't looked into TPMs, but the other two seem to be the standard way to go.

Now, if additional hardware is out of the table, I can see that your approach makes sense in general. I would worry for the way in which each copy of the key is handled (encrypted and unencrypted, in RAM and in disk, in active usage and in backup), and the way in which the password is used for encryption. In particular, the less the key exists in plaintext, the better.

But mind the threat model. Knowing what you are concerned about is key to know whether your defenses are actually defending you.