Gisele, you've done a great deal of thinking about a very special and very rare kind of construction. I'll try to address your major points. Your first sentence, and the one you were in doubt about, is
Were the police to have found out, I would have been in trouble
This is a perfectly grammatical sentence, with its perfect infinitive "to have found out" indicating a "finding out" prior to the established past time frame of the situation. In other words, the scene is already in the past, and the conditional idea refers to a previous time.
The progression of the various forms from informal to hyperformal is the following:
1) If the police had found out... (standard version)
2) Had the police found out...
3) If the police were to have found out...
4) Were the police to have found out... (hyperformal version)
"Were the police to have found out" is, if I may say so, the most "baroque" version of the simple conditional "If the police had found out...."
Before going any further, let me offer a statement about the frequency of the inverted conditional constructions with "had,"and "were" (also "should," which I won't talk about here). On this point Biber et al.* state:
"In conditional clauses with had, were, and should, it is possible to mark the adverbial clause with subject-operator inversion, rather than use the subordinator if:
Had it not been for human kindness he would have ended up in a pork pie (NEWS)
Were he to deflect the challenge by dissolving parliament, it would confirm he had not properly learnt the lessons of April's disturbances (NEWS)
Should the patient be the person who had attended to the business and financial side of family life, then there will have to be a reversal of roles.
"Each of these three conditional clauses could be introduced with the subordinator if used with regular subject-operator order. " (pp.851-2)
They then give the frequency counts for the inverted forms vs. regular forms in four genres (registers):
"In all registers, conditionals with had and were are very rarely marked by subject-operator inversion...." (p. 852) (Note: Had and were were counted separately from should. MM)
The frequency statistics given for inverted had and were in three registers"”conversation, fiction, and academic writing"”are so low as to indicate that these forms hardly exist. The frequency of both forms in the register of news is only about five percent.
So the construction you're asking about is very rare indeed. Here, nevertheless, are a few examples from Google:
"”that is what that particular statement suggests is that there would be support were they to decide that this was not the best course of action to take. ...
"” judicial expertise and one would think that it would reflect badly on themselves were they to agree that troops under their command had commited crimes. ...
"”and then once they come for medical treatment, the treatment is not as effective as it could have been were they to have come earlier (Tr. 7649-50). ...
"”IQ) and neurocognitive development, thus indicating their testing methodologies could have detected mercury effects, were they to have occurred. ...
"”But it's probably also worth pointing out that were you to have asked in the 1920s how the work on quantum mechanics would affect the world, I don't think people would have had much to say.
You can see from these examples that the style is formal.
A sentence like "Were he to have plastic surgery..." is, as you surmise, about a hypothetical future action. (For some reason I don't know, it can't be used with a hypothetical present state, e.g. *"Were he to have dimples.") "Were I to have [drawn up a different contract..."] is about a hypothetical past. "Were he to have had dimples" is, at best, questionable.
You also ask about "Were it not for the fact that...." This is a separate issue. It talks about the existence of a fact, not about the existence of a situation or the performing of an action. It stands outside the basic two ideas in a conditional, one step removed.
It's important to note that in many cases, the phrase "the fact that" is redundant"”extra baggage. It should be avoided except where necessary for the meaning of the sentence. A conditional sentence can usually be created without resorting to "the fact that." If you do produce a conditional with "the fact that," you have to know that there is a time difference between these two conditional clauses:
Were it not for the fact that... = If it weren't for the fact that... ("now," hypothetical)
Had it not been for the fact that... = If it hadn't been for the fact that... ("then," hypothetical)
I hope that these thoughts have answered your concerns, Gisele. If you're still in doubt about something, please let me know.
*Biber, D. et al., Longman Grammar of Spoken and Written English (1999)