With a hotplate stirrer you don't need a separatory funnel, assuming you filter the bark out before you basify the solution.
Add the non-polar solvent to the basic water, create a vortex, wait a bit. Stop the stirrer, wait for the layers to separate and emulsions to settle (happens quickly if the pH is 13+ and the liquid (not surface) temperature is 60-70C). Use a pipette or syringe to collect the solvent layer. Repeat several times and you are done.
The heat will help the yield, reduce the amount of solvent required, but will also decrease the purity.
Safety tip: you do not want any lye splashing out. So avoid any extremes: do not cap the vessel airtight, do not go crazy with the stirring speed, do not heat the solution up to boiling. Leave some headspace in the flask and break up the foam if starts blocking the vapors.
Purity tip 1: The layers do not actually separate fully - there will be tiny droplets of water in your non-polar solvent (and vice versa) - the closer to the separation line, the dirtier the solvent is. It means you will end up picking up some water and lye particles even if you are extra careful. (This is why dryteks produce cleaner DMT than wet teks, by the way - liquids separate from solids much better than they do from other liquids). To minimize that contamination stay as far away from the separation line as you can (especially since you will keep adding more solvent anyway). Transfer the solvent to a tall measuring cylinder first, and wait for any gunk, visible and invisible, to sink to the bottom. The top part of the cylinder should be good enough to transfer out. The cylinder is reused, so you will not lose much overall.
Purity tip 2: I recommend defatting after you filter the bark out. Just follow the same exact procedure a few times; here instead of DMT you will extract plant oils and other non-polar impurities. Since the solution is still acidic, the emulsions will take much longer to resolve.
Purity tip 3: I also recommend a sodium carbonate + water wash before you finally evaporate and/or freeze-precipitate. It can be done in a smaller flask, with manual swirling. It will reduce the yield, so if you have never done it before - skip this step, collect and weigh the final product first, and then redissolve and wash it to see how much you lose and if you are OK with that.