Are there ways to increase the rate at which humans can output information?

I see your point, and I would argue that both the rate of output and quality of output matter. You're right that one doesn't necessarily count without the other. A human could produce hundreds of gigabytes of pseudo-random numbers with a single key press, but that output could hardly be classified as 'information'. To classify any data as information, it has to represent some meaning that can be discerned by a receiver with at least some degree of fidelity. Humans do appear to be limited in our ability to produce information at high rates.

The underlying message here is very important to consider in this discussion. In many ways, the average human may already be outputting intelligent information about as fast as he or she can. If we really could think substantially faster than we can speak or type, then surely we could speak in mathematical formulae and in beautiful poetry at all times. When solving a complex mathematical problem, it seems most people have to stop and think periodically while writing steps and results. The processing is slower than the output. The main area where most humans are quick seems to be in visuospatial cognition, and this is perhaps the main area where we lack proper output capabilities. We need a parallel output system to complement the current serial output. Maybe if we had 64 mouths and ears we could convey information more quickly. Alternatively, a high resolution EEG could perhaps read all our muscle tones simultaneously. The tricky thing would be in training ourselves to output with all our muscles simultaneously, and the result might be a show in itself.

Yes, I'm wondering if there is any potential for leap frog advancements.

In this case, thoughts do seem to be the upper bound. If we are talking about linear streams of vocalised thought, then I suspect we might not get much further from where we are. I, for one, find it harder to stream thoughts faster than I can talk.

But consider any highly complex communication task. For instance, say you have to explain how recursion works. You have to go through abstract thinking, analogising, structuring, word selection, and delivery. It's hard work, and unless your execution is spot on, vital information maybe lost in transmission. Importantly, your thoughts here may not be a linear vocalised stream, and the process may not take very long.

It seems that tasks like these would benefit from some form of information exchange mechanism that doesn't rely on information being encoded in present day language. It would be most efficient to somehow "compress" your thought process around recursion as you're thinking about it, and then have the receiver unzip it on reception.