Firstly I am by no means an expert at mushroom cultivation but have been playing around with some ideas since last summer. Shiitake seems to prefer hardwood logs or sterilized woodchips/saw dust, 'tried, tested and true'. I have done quite a few logs and a couple of totems outdoors with meh results which is my fault for not caring for them 100% in the extremely dry hot summer.
I have had luck using straw to grow shiitake in sterilized straw using 'LE-straw from Aloha Culture Bank' strain, albeit not great results using lime soak/cold pasteurization i have used for Oysters. This specific culture is extreme fast growing but prefers fine shredded and heat sterilized straw. Sadly not the same results in straw with couple of other shiitake strains but have known others who have had better luck with them. I used Wood chipper shredded straw pressure cooked at 15 psi for 1 hour minimum, inoculated with 5% grain spawn and 3% gypsum in a clean glove box, saw full colonization under 20 days and browning a little later in rough desert summer in 60-95 degree indoor temperature(shitty 60's trailer with no insulation) with loss of 2 out of 12 bags to signs of mold.
I have linked below the cultures and if you read their website they have some great DIY and professional tips and techniques.