In some cases there is an alternative to worrying about latin plurals; find a real English word instead. So sometimes we can use "hallmark" or "benchmark" instead of criterias, or hallways, or even foyers instead of atriums, just avoiding the issue.

There must surely be more to education than a head stuffed with latin plurals.

I cannot think it a good preparation for those school-leavers of 1944 who were drafted into Klever Reichswald where a subaltern's life expectancy was just three weeks.

A good beer and a shag might been more use than conjugations. Surely education has more to do with overturning moribund thinking than following the posturing of a bygone era.

@Brus Oddly, English borrows words quite freely but we seem unwilling to anglicize them properly, or at least it takes some time. The truth is that trying to impress people these days with one's "private" schooling and superior knowledge of Latin and Greek is likely to backfire and make one sound like a pratt.
Some other languages are more pragmatic about borrowed words, respelling them to fit their own orthography and changing the endings to conform to their own grammar. So 'bus' in Hungarian is spelt 'busz' (as 's' alone sounds like 'sh') with plural 'buszok'. This approach makes more sense to me.

Russian generally does the same but there are a few exceptions like the word for overcoat пальто which are just indeclinable. The trouble in English is the snob-value of latin endings.

@WW more examples to ponder (from IELTS task 1)
"....along with plummeted output of fertilizer..."
"....along with decreased output of fertilizer...."
"...along with dropped output of fertilizer...."
"....along with fallen output of fertilizer...."
"...along with reduced outptut of fertilizer...."
The tricky one is increase/decrease which flips between intransitive and causative transitive.
Seems to be more of an issue for SNAILs* than euro-language speakers.
SNAIL = S-peaker of N-ot A-n I-ndo-european L-anguage

Whilst acknowledging Hewins' list, my take is that all the pp of all transitive verbs is at least potentially a before-the-noun adjective, given meaningful context.

"The provided information" does come up on google, although I would would write "the information provided".

Dragging a "transitive" pp forward does not automatically create gobbledegook, whereas dragging an "intransitive" pp mostly seems to break syntax, unless it is already well-established, or ends in "-n", or has an alternative (but unmarked) transitive causative meaning which fits the context.

Local immigration here demands IELTS 7.5 (min 7.0) for all professionals like teachers, doctors and so on ; or CPE. Unfortunately the band 7 writing descriptors include the criteria "uses less common lexical items with some awareness of style and collocation" and "produces frequent error-free sentences"; so this is quite a hurdle for SNAILs. But like in CPE, background reading is sine qua non, and writing scores tend to be below reading scores.

By "a hit single" I meant "a loved woman"
"a cooked egg" also comes up

@WW yes it works better with longer/latinate words.
It is interesting to google the example phrases - "a bitten man" , "a hit dog", "a hit single", "a told joke", "a sent letter" all came up.

www.glcon2013.org/wp-content/uploads/2013/09/paper_18.pdf

@WW yes you've got the issue
Apart from a few verb pairs like rise/raise, fall/fell, the intransitive/transitive is not marked in English (whereas in Hungarian there are many such verb pairs) - and the meaning tends to slide toward a causative. So if the pp is used as an adjective the meaning usually comes from the transitive, as in "a raised bench", "a felled tree" vs "a fallen tree".
My guidelines are pretty much the same as yours:
1) You can usually use the pp as an adjective before the noun but some must come after - there is a list of common exeptions in "Advanced Grammar in Use" (Hewins) I think.
2) In this context beware of intransitive-only verbs!

@WW yes the standard view of "reduced relative clauses" is fine. [Santa's children?]
What I'm looking for is guidelines for when it is okay to drag the pp before the noun and use it as an adjective there. Thus:
1) "The selected players will start training today". - OK.
2) "The maximum number of standing passengers is 26'. - OK
3) "Discouraged students trail behind." OK
4) "A declined offer cannot be the subject of a counter-offer." OK
5) "Encouraged students learn better." (??)
6) "Declined numbers of students are expected next semester." (?)
7) "Withered flowers should be removed daily." OK
8) "A failed marriage" , "A crashed plane" "Grown men" - OK (tho pp is clearly not passive in meaning)

Ah I do get a few hits on google for "disappeared species" and "unthought consequence"

@WW Yes I am with you there.
It is tempting to overgeneralize and say that one can use the pp (or third form) of a transitive verb as an adjective; but in fact many would be rarely used in this way. For example "a thanked woman" sounds unusual to me.
The other thing is that the 'rule' (that the pp as an adjective has a passive meaning) doesn't quite hold up, as with "piled-up leaves" , although it is true that intransitive verbs rarely form an adj from the pp - "a fallen woman", "the risen Christ" are other examples.
"A disappeared species" - no ; "a vanished species" - yes
"a well thought-out plan" - yes; "an unthought consequence" - rare if at all
All seems pretty random to me.