Finasteride would be useless for your situation as your hairloss is not due to DHT. I lost a ton of hair in a diffuse manner as well due to my thyroid going out of whack a year ago. I would stay away from Synthroid as many people report hairloss while they're on it. I've started taking Iodoral...
https://www.hindawi.com/journals/isrn/2012/823875/
Figure 1: NCI8642 is able to abolish DKK1-LRP6 interaction at the cell surface. (A) Immunostaining of DKK1 on HEK293 cells (panel a), on HEK293-LRP6 cells (panel b), on HEK293-LRP6 cells in the presence of 1% DMSO (panel c), and on HEK293-LRP6...
As you stated, this is only a "cure" for you as it would really only make sense if you had elevated level of testosterone before which would result in overall more DHT. Now, the same would not work for many others as people bald even though they might have low testosterone as their follicles are...