Polite/professional alternative to 'It turns out'
Solution 1:
I think that if you explain the reason(s) why you cannot do (...) or you don't (...) you can use "as a result".
Perhaps you could start saying "Unfortunately, taking into account that ..., we are sorry to say it is not possible for us to..."
I hope you find my comment useful.
Good luck.
Solution 2:
As it happens...
We have found (alternatively: discovered/realized)...
It seems...
We must (alternatively: regret to) inform you...
The (add one of these if desired: simple/unavoidable/unfortunate) fact is...
Ultimately...
In the end (alternatively: last analysis/long run)...
The upshot (alternatively: result/final determination or verdict) is...