Can I get a L-six months without invitation letter or with one from a daoist temple?

To apply for a L, you can offer invitation letter from a Chinese organization or a permanent resident or air ticket booking record (round trip) and hotel reservation. But you may not stay for six months with it.

I suggest you apply for a F. But you have to prepare "Invitation Letter of Duly Authorized Unit" or "Confirmation Letter of Invitation". For more info about F:
https://www.travelchinaguide.com/embassy/visa/business.htm

you can apply business type, and offer china invitation letter to embassy.