This would require a more stringent set of pulse widths that matches the response of the rest of the circuit. That could be hard to achieve so a controller chip is probably the best bet now.I did implement your first suggestion. But it didn't make a difference. Am I making an error somewhere in understanding or implementing, I'm not sure.
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I did try 1us though, and I see the output did go up to a lower value, but then at some point a wider pulse would be required to get up higher in a shorter time period, then another wider pulse, then another, etc. The pulses cannot be selected arbitrarily though they have to be matched to the output circuit. That means this may not work very well because it would be hard to match the output to every load.