The problem here is that the TA should never have undertaken to change a ticket within hours of travel as it is at that point under BA's control and the TA could not have reissued it. But, when the TA undertook this, all of OP's problems flowed from that.

OP should simply return to the TA and have the TA fix the issues. Bottom line, OP should be restored to whatever it is that he should have paid for his newly-issued Saturday flight.
Let the TA and BA slug it out and the TA issue the proper credit to OP.

As a general suggestion, I would not have a TA issue a simple short-haul ticket such as this. It adds a level of complexity and when things go wrong, it is more difficult to fix.