What is the difference between 'try' and 'attempt' when used as nouns?
Solution 1:
There is actually a use of try that would allow "It was a try at ...", but it's informal, and being informal some people will not use it, and few would use it of a speech that aimed "to pacify all parties concerned". Informal uses tend to be less universal than formal uses, as different people make different choices as to which informal uses are "incorrect" and this creates localised variations in use.
You can find examples by looking here and then excluding those which are using try in the rugby sense of the word.
The use of try that doesn't state what was tried, but implies it from context, is also less formal, but more commonly used, and hence less strange to your ears.
Conversely, the informal stab is the opposite:
I made another stab at it.
*I made another stab.
Ultimately, this just comes down to the definition of the words, in different registers and dialects. The definitions of stab include one where it means an attempt at something referred to, but does not include one where it means an attempt at something implied. The definitions of try include an attempt at something implied, but in many versions of English do not include an attempt at something referred to.
Solution 2:
The word an attempt has connotations of difficulty, whereas a try does not, simply!
the act of trying to do something, especially something difficult: [+ to infinitive]
She made a few half-hearted attempts to join in their conversation.
He made no attempt to be sociable.
This is my second attempt at the exam.
None of our attempts at contacting Dr James was successful.
They closed the road in an attempt (= to try to) to reduce traffic in the city.
definition of attempt and example sentences on Cambridge Dictionaries Online
The structures are an attempt at something and an attempt to do something… the preposition at is not used when attempt is followed by another verb, in the full infinitive.
[C usually singular] an attempt to do something:
They might still have tickets left - why don't you give it a try?
This will be her third try at jumping the bar.
You could ask him if he's willing - it's worth a try.
definition of try and example sentences on Cambridge Dictionaries Online
The structures are a try at something and a try at doing something… the preposition at remains, and that's why the following verb is in the gerund.
Using try does not mean that the thing attempted is not difficult but simply that the idea is not especially present in the speaker's mind, whereas it is when they use attempt.
The definition of try tells you the noun is usually singular, so if you want a plural, you will tend to use attempt instead, which is not illogical —come to think of it— since if the first try is not successful, then the thing attempted must have some difficulty in it, and the failure makes you aware of it, hence attempt and no longer try.
I ngram-viewer-ed several tries and several attempts: several attempts appears to be more common.
ngram viewer for the noun phrases several tries and several attempts