If I call a company and I get a recording on their end that states the phone call may be recorded, doesn’t that imply their consent to be recorded? So I should be able to record the same phone call with both parties “implied” consent!

I agree, they KNOW they are being recorded! If they don’t want to be recorded then they have the option of not taking the phone call… or course they will probably be out of a job!

There are only about 12 or 13 states in which you need consent of all parties before recording a conversation.

The fact that one party consents does not in any way mean the other parties also consent.

If they say: "Calls may be monitored or recorded for quality purposes." You then say, "Okay, If you want to record me, can I record you for my own quality purposes?" If they say no, then ask them to stop recording or hang up.

No...not implied consent since you are not giving them the chance to hang up. You provide implied consent by continuing the call.

I disagree. They are notifying you that you may be recorded. That doesn't imply their consent for you to record them. You'd have to request their consent to do that.

Absolutely not. Any party recording the call must inform the other.