Rather then doing "another" petition, how about writing to TfL or getting a councillor/MP on side to write a letter laying out the reasons for its need and the impact on those who cannot negotiate the stairs and the inconvenience experienced in having to go the long way round.
This sounds like a very sensible suggestion, samuelsen. It's not 'weight of numbers' that will secure the necessary funding but 'weight of argument' - and the political weight of the people making that argument.
Are there any appropriate local charities/support groups that would be on side for this?