Hi. I do not have specific experience with Septobasidium spp. but I did work with DNA of a basidiomycete. I just used standard guanidine thiocyanate method with very gentle chloroform and isoamyl alcohol washes later. This involves grinding the biomass in liquid nitrogen and processing it the lysis buffer and centrifugation steps to isolate and wash out the DNA.
The key is to be super gentle and keep the sample cold throughout the extraction if you desire to obtain high molecular weight genomic suitable for genomic sequencing. This can be verify by running a simple slow electrophoresis gel and see if you get a smear or a clean heavy band. Primitive but works.
As for isolation method, you will have to find out the nutrient preference for your fungus of interest and how to separate it from the background. I hope this helps.