If I was going to experiment with a new extraction method, my choice would be to acquire a soxhlet extractor, and experiment with ethanol as a solvent, for producing budder. https://www.erowid.org/archive/rhodium/pdf/soxhlet4dummies.p..., page 2 shows a DIY version that doesn't require you to purchase glassware. I would recommend putting the whole setup in a larger pot of water, so that you can more easily control the temperature. You can use the same setup as a still, to extract ethanol from something like cheap vodka.
As for methods that I have actually tried, cold butane extraction produces spectacularly clear oil, which eventually dries to shatter. Do freeze the weed first, don't freeze your hand. Do leave the extract spread out in a thin layer to evaporate until it forms hard shatter, otherwise some very scary butane will remain in the product.