Hi alexzive,
Expressions “so to speak” and “in a manner of speaking” are similar. But I don’t think that “let’s say” is the best substitution for them. No. Let’s say means to assume.
So to speak is often met at the end of the sentence. I think your sentences are fine but with different meanings.
Let’s wait for our moderators
As Pamela said, yes, you can also use the expressions in spoken English AND the expression ‘so to speak’ is normally at the end of a sentence. I would not place it at the beginning.
A similar expression to ‘so to speak’ is ‘as it were’.