I think the easiest way is to not make it really "dynamic" but an append-only structure of static content. For example a Reddit thread might be representable as a static list of actions (add reply, upvote, downvote, etc), which the client would process to get the current state.
That way, you could immediately download an earlier version of a resource and then get the updates as they spread through the network.
They have a big problem in their design where currently it works exactly as you described, and at "some unknown point in the future" when the database of all transactions EVER in the history of bitcoin gets too big for each person to have to have a copy of in order to add another transaction, they'll "figure out a way" to make it unnecessary.
Can't they somehow publish the current state of things, let anyone who wants to verify it from the public record building a web of trust, then go from there forward?
That way, you could immediately download an earlier version of a resource and then get the updates as they spread through the network.