The more effective method for lipid extraction is the solvent extraction using Hexane. It can be easely recovered by distillation and reused in the process. All seed oil on the market are extracted in this way. If oxidation must be avoided, the solvent removal could be carried out usig vacuum and low temperature. The only inconvenient is that the matrix must be dry.
I’m pretty sure that you are aware of the overwhelming amount of literature available on this nowadays so relevant and important issue you address.
Personally I find the following reference (which you probably know) interesting (it gives a good overview on the current status):
Ramluckan, K., Moodley, K. G., & Bux, F. (2014). An evaluation of the efficacy of using selected solvents for the extraction of lipids from algal biomass by the soxhlet extraction method. Fuel, 116, 103-108.
A more than excellent review pointing out the different dilemma’s and shortcomings of the current methods is:
Katiyar, R., Gurjar, B. R., Biswas, S., Pruthi, V., Kumar, N., & Kumar, P. (2017). Microalgae: an emerging source of energy based bio-products and a solution for environmental issues. Renewable and Sustainable Energy Reviews, 72, 1083-1093.
Coming back to your question it seems to me that dry matter is the way to go (although my initial thought would be to use wet material). For now solvent extraction based on (modified) Bligh & Dyer method is the best.
However as stated for example in the above mentioned review this is still far from perfect.
Good luck with your quest to a better and more ‘perfect’ method.