How can I "cheat" on dough maturation?

The easiest method, and most common in a commercial setting, would be to add a small amount of yeast in addition to the sourdough starter. You will probably have to reformulate a bit, as the dough will mature faster leaving the starter less time to develop flavor. This is usually overcome by also increasing the proportion of starter (and adjusting the final dough's hydration based on the hydration of your starter).

For instance, if your original recipe included 30% starter (in baker's math), the faster version might have 40% starter and .5% yeast. If you use a liquid starter, you may then cut the water by 5% or so, and if you use a solid starter no further adjustment may be needed.

You didn't specified the preparation steps of your recipe, so I don't know if you already doing what I'm going to suggest. It's from Max Berstein's post on Serious Eats and I don't know if this tip will work with sourdough starter:

Mix first only flour and water, nothing more, until all flour is incorporated and let it rest for at least 15 minutes. Them you add the yeast and salt, knead until all ingredients are incorporated.

From my (small) experience, I found this to make the dough rising more efficient, in only a few hours the dough doubled the size. If you didn't do this already, give it a try.

The reasons for not adding salt and yeast at the beginning:

Although salt strengthens our gluten network overall, it's also very water-hungry. If we added salt to our autolyse, it would compete with our proteins and starches for water, causing them to take longer to hydrate. While this wouldn't be a disaster, we've already committed ourselves to a five-hour project here, so why make it harder on ourselves?

And as for the yeast, its job is to ferment our flour, causing the bread to rise and develop flavor. But on a chemical level, mixing—and autolysing, in particular—isn't about flavor. It's about structure. Were we to put our yeast in during our autolyse, it would start belching out gas. When we begin our kneading steps later, we would just end up pounding this gas back out. In short, the yeast just doesn't have a job to do during the autolyse.