It seems to me you could just use static ACLs and create (or not) object names to cause this 403 vs 404 distinction? The drawback is that you'll be paying for the minimum retention of minimum-sized objects, not to mention all the other bucket management traffic you are using.
So you're going to have a lot of consumers of the same bit stream before you've somehow made the covert, "free" egress a net positive value versus a regular object. I imagine AWS can trivially put in place some throttling of error responses to make this impractical.
Ignoring these economic issues, imagine a content-addressing scheme like /stream-identifier/bitnumber which you can then poll to fetch one bit per request. Populate an object (which will return 403) for 1 bits and omit an object (which will return 404) for 0 bits.
You also need to know some stream length or "end of stream" limit. Otherwise you can't tell if you've read past the end or are really fetching 0 bits of a longer stream.
One strategy might be to use an 8b/10b encoding so you can detect when you're not getting a valid symbol anymore. You could treat that as end of stream if it is supposed to be static, or go into some polling mode to wait for more symbols to be posted.
Hybrid strategies might use regular objects or recursive use of these streams to publish metadata streams that tell you about the available stream names, lengths, and encoding schemes.