Can I ask what you mean by A >> B? Do you mean upstream or higher expressed? If transcript ends are under-represented, wouldn't a downstream alternative TSSs site stick out in relation to its (upstream?)surroundings, as it is a transcript start and not end? Perhaps I misunderstood something.
I do agree that the data type is not very suitable for the task. Something that maybe could work is finding already known alternative promoter sites and checking those for their expression levels at the various possible TSSs, as you thus include some prior knowledge.