Is it valid to repeat the Jumu'ah prayer with a new sermon after a prolonged interval between the first sermon and the prayer due to an error by the Imam and the combining of the Asr prayer and consultation, or would it have been sufficient to perform it without a sermon?

If you are certain that the Imam's prayer was invalid, you must instruct him to repeat it. If he does not comply, then repeating the Friday prayer is valid if your number reaches the recognized quorum for its عقد, otherwise you should repeat it as Dhuhr. What you did by repeating the Khutbah (definition) is correct, to maintain continuity between it and the prayer. However, the Asr prayer you performed with the Imam is not valid due to lack of sequence, and because some scholars do not permit combining Asr with Jumu'ah.