There is no legal time limit for a tribunal judge to produce a statement of reasons. I think one to two months is typical.
I can remember reading this thread when you started it two months ago. I'm sorry to hear of the outcome of your appeal, but I'm pleased that you now have an advisor who can help you proceed.
early last year, it took them 16 weeks to send me my SOR. every time i phoned asking where it was, i was told it was ether in the post, it's going to be sent out and the judge had left the UK.
I think the law actually states that a statement of reasons should be sent within one month of application or as soon as is reasonably practical. What is meant by reasonably practical is anyone's guess.
In the past an appeal to the UT on the grounds that the first-tier tribunal took too long to produce a statement of reasons was dismissed, but the Commissioner did state that an SOR that takes more than (I think) six months to be sent is to some extent devalued.