Call TFL and ask for the video, they will send a DVD in the post and put the penalty on hold while you wait.
One possible angle we haven't explored before is that under
section 15(2)(c) of the Greater London Council (General Powers) Act 1974 "A local authority may prosecute in respect of any offence under the foregoing subsection which is committed in its area", every other reference to an authority is to a highway authority, which is defined as:
“highway authority” means the Secretary of State in respect of all trunk roads, Transport for London in respect of all GLA roads and a borough council or the Common Council, as the case may be, in respect of all streets in their area, whether or not maintainable at the public expense, which are not for the time being trunk roads or GLA roads;
The fact that different terms have been used indicates that the power to prosecute rests with the local authority, irrespective of who the highway authority happens to be. Unless decriminalisation changed this, the consequence would be that only the local authority can enforce, and TFL cannot.
Obviously this is a novel an untested argument, but food for thought.