convert Bouncy Castle's AsymmetricCipherKeyPair (RSA) to java.security.KeyPair

I am trying to automate generation of CA and certificates for our E2E testing. I started with Bouncy Castle and I have managed to generate CA cert and machine cert. However, now I need to convert the RSA keypair represented by BC' org.bouncycastle.crypto.AsymmetricCipherKeyPair to java.security.KeyPair. I cannot seem to find a way to do this.

There's probably more than one way to do it, but here is one example:

import org.bouncycastle.crypto.AsymmetricCipherKeyPair;
import org.bouncycastle.crypto.util.PrivateKeyInfoFactory;
import org.bouncycastle.crypto.util.SubjectPublicKeyInfoFactory;
    
import java.security.KeyFactory;
import java.security.KeyPair;
import java.security.spec.PKCS8EncodedKeySpec;
import java.security.spec.X509EncodedKeySpec;

private static KeyPair convertBcToJceKeyPair(AsymmetricCipherKeyPair bcKeyPair) throws Exception {
    byte[] pkcs8Encoded = PrivateKeyInfoFactory.createPrivateKeyInfo(bcKeyPair.getPrivate()).getEncoded();
    PKCS8EncodedKeySpec pkcs8KeySpec = new PKCS8EncodedKeySpec(pkcs8Encoded);
    byte[] spkiEncoded = SubjectPublicKeyInfoFactory.createSubjectPublicKeyInfo(bcKeyPair.getPublic()).getEncoded();
    X509EncodedKeySpec spkiKeySpec = new X509EncodedKeySpec(spkiEncoded);
    KeyFactory keyFac = KeyFactory.getInstance("RSA");
    return new KeyPair(keyFac.generatePublic(spkiKeySpec), keyFac.generatePrivate(pkcs8KeySpec));
}

And here is an example to go in the other direction, to convert a java KeyPair to a Bouncy Castle AsymmetricCipherKeyPair.

private static AsymmetricCipherKeyPair convertJceToBcKeyPair(KeyPair javaKeyPair) {
    RSAPublicKey javaRsaPub = (RSAPublicKey) javaKeyPair.getPublic();
    RSAKeyParameters bcRsaPub = new RSAKeyParameters(false, javaRsaPub.getModulus(), javaRsaPub.getPublicExponent());
    if (javaKeyPair.getPrivate() instanceof RSAPrivateCrtKey) {
        RSAPrivateCrtKey javaRsaPriv = (RSAPrivateCrtKey) javaKeyPair.getPrivate();
        RSAKeyParameters bcRsaPriv = new RSAPrivateCrtKeyParameters(
                javaRsaPriv.getModulus(),
                javaRsaPriv.getPublicExponent(),
                javaRsaPriv.getPrivateExponent(),
                javaRsaPriv.getPrimeP(),
                javaRsaPriv.getPrimeQ(),
                javaRsaPriv.getPrimeExponentP(),
                javaRsaPriv.getPrimeExponentQ(),
                javaRsaPriv.getCrtCoefficient()
        );
        return new AsymmetricCipherKeyPair(bcRsaPub, bcRsaPriv);
    } else {
        RSAPrivateKey javaRsaPriv = (RSAPrivateKey) javaKeyPair.getPrivate();
        RSAKeyParameters bcRsaPriv = new RSAKeyParameters(
                true,
                javaRsaPriv.getModulus(),
                javaRsaPriv.getPrivateExponent()
        );
        return new AsymmetricCipherKeyPair(bcRsaPub, bcRsaPriv);
    }
}