A little late to respond I suppose, and you’ve probably already arrived at this conclusion on your own, but I would suggest looking at a couple of examples of recent stories you’ve created and working backwards about how long it took you to get through the story development from start to finish and note the differences. For example, if someone is requesting a reference for a product that hasn’t even launched yet and there’s no beta (personal favorite 😏 ) vs a reference that squarely lines up with a popular use case/solution etc (bread & butter). Maybe create some tiering based on business segments, solutions, and types of requests.
Another idea is to ask requesters to show what the business impact is so you can help prioritize and have a sanity check. If your team is hyper focused on 3specific products or company goals, for example, creat SLAs for requests that are in line with them and an explanation for timeframes for requests outside of those.
I love working cross functionally - it’s one of the best parts about advocacy but it’s easy to get drained by the volume and urgency!