PS. Due to the timeframe, I think a CC chargeback may be out of the question.
I understand that 18 months is closing in on the usual maximum timeframe ... though there may not be any actual limit legally speaking.
Seems pretty clear cut to me, but you will, of course, know the subtlety of it all. Sounds like you entered a contract based upon verbal assurances that proved false and that you didn't get an opportunity to see the T&C until after money had changed hands.
The companies "cooling off period" is meaningless legally speaking, insofar as I understand these things. Its no more than a voluntary undertaking from them and shouldn't in any way impede the progress of a charge-back where they need to show cause as to why the charge back shouldn't occur. Sounds like you have names and dates as well as a written log of the telephone sales call. Diary entries are often sufficient in cases like this.
If the company doesn't have written or recorded evidence, and you do, I can't see how you'd lose. Even if they do have a recording, the interpretation of this is for a court ruling (probably... or mediation), but this is an entirely separate action to the charge-back and is for the company to pursue, not yourself as the case then becomes one of non payment for services rendered (ie, them versus you).
If you word your application correctly, it should boil down to: Did you receive goods or services per the contract? The company must show cause that you _did_ because you will maintain in your charge-back application that you didn't.
The bank won't even try to be a mediator in this. All you are doing, after all, is rescinding payment. There is no pleading of a case, no judgement of right or wrong on behalf of the bank. Once payment is successfully rescinded the matter then becomes one of contract law / consumer law. Did you receive contracted goods/services? Both sides to plead their case in court and action to be brought by the company as their case will be that you didn't pay them (because the payment was rescinded).
If nothing else it should provide you your moneys worth in entertainment and education value at essentially no additional cost. You may also elicit some small satisfaction that in so-doing you will wind up the companies "machine", at some effort to them. More commonly, in cases like this that I've heard about or been involved in, the business won't even respond to the banks show cause and by default you'll get your money back.