subject operator inversion - conditionals without if


I'm aware that in conditional sentences without the conjunction "if" an inverted structure may be possible, such as in,

Should you need more details, let me know

Had she known about it, she would have left

Were I in your place, I would be very happy

Were they to try, they would succeed

My current doubt is related to the "were" sentences. First of all, besides the simple infinitive structure, is it ever possible to use a perfect infinitive?

I read a posting in another forum with a sentence that confused me:

Were the police to have found out, I would have been in trouble

Is this sentence grammatically sound? It seems strange to me. Is it as good as "Had the police found out, ..."

My feeling was that the were-sentences with infinitives could only happen in the second conditional - "Were the police to find out, I would be in trouble" = "If the police were to find out, ..." - Does this mean exactly the same as "If the police found out, ..." ?

Isn't there often (usually / always ?) a kind of vaguely future connotation?

If I were to take up a new hobby, I might go into photography
(If one day I were going to take up / If one day I took up...)

It seems to me that the inverted structure is not possible in the third conditional, or when the 2nd conditional is a comment totally based on a present situation.

For instance,

* You didn't go, you didn't meet Bob
If you had gone, you would have met Bob
?? Were you to have gone,... ??

* He does not have dimples; he's still cute
If he had dimples, he would be even cuter
"Were he to have dimples, ..." .

Then again, I think we could say, "Were he to have a plastic surgery and gain some dimples, he'd..." = If one day he were going to have... = If one day he had...

Considering the issue of time, and trying to create a sentence where the inverted structure with "were" does not apply to the hypothetical future, I could only come up with the wordy, rather clumsy subterfuge of saying "were it not for the fact that", which in some situations may allow us to refer to the past, the present and the future.

Were it not for the fact that it rained, it would have been a perfect day

Were it not for the fact that he is too young, he would be the best candidate
(Were he not so young, / were he older, he'd be...)

Were it not for the fact that they will not hire more people, I doubt they would be able to finish the project
(Were they not to hire more people, ... / were they to keep the same number of people, ...)

In fact, though I've been trying to feel and understand the structure better, I'm still not very confident using it.

As usual, I'd be most grateful for any comments.

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