Welcome to Flyertalk and welcome to the BA forum. If nothing else positive comes out of this, at least you now know where to get independent and free advice about travelling on BA as well as redeeming Avios.
I'm sorry to read about this, but if you look at it from BAEC's perspective, this does have a lot of red flags all over it. I'm personally not at all surprised that BA came down like a ton of bricks on this. Almost all Avios transactions are done - and are supposed to be done - by the cardholder directly or a family member. At a pinch - this would now be unusual - your secretary or admin assistant. But using an external body to manipulate your account, and many others, has the hallmarks of trading off one set of inventory (redemption inventory) against cash inventory, so your Avios actually being used to help someone else for cash, and some of the cash being used for your requirements. That's how it was a "better" itinerary for you, but certainly not a better itinerary for BA.
I don't see any point in complaining to BA since they will presumably just say "this is not in line with BAEC's terms and conditions" - you have to get the travel agent to remedy the situation. It may be that BAEC will allow you a new account for the future, but it wouldn't have surprised me if BA simply banned you for life. See below, my bolding. Other clauses make it clear that Avios are personal and your relationship is with IAG companies.
Originally Posted by BAEC Terms and conditions
22.1. Except as otherwise provided by British Airways and AGL and communicated to the Member, Avios points are not transferable (whether from person to person, account to account, statement to statement, card to card or otherwise) other than in accordance with the Conditions of Use and cannot be bequeathed, devised or otherwise transferred by operation of law.
22.2. Any purported purchase, sale, transfer, unauthorised use (including bartering), procurement or redemption of Avios points issued or awarded to another person or any other use of Avios points contrary to these Terms and Conditions will constitute a fundamental breach by the Member of these Terms and Conditions and the Conditions of Use.
22.3. Each Member acknowledges that a breach pursuant to Clause 22.2 above may also constitute an inducement to breach the contract among British Airways, AGL and the Member, intentional damage to the business of British ;Airways and/or AGL, or conspiracy and criminal offences under the applicable local or national law. Any breach pursuant to Clause 22.2 will constitute Fraud and/or Misconduct and will be dealt with in accordance with Clause 24.