I think Collins misses the mark by calling "even" an expression of surprise. "Even" is sort of an all-purpose intensifier, and is actually pretty hard to nail down. The OED's definition I think gets pretty close (but its length is an indicator of how fuzzy the word is):
- Intimating that the sentence expresses an extreme case of a more general proposition implied (= French même). Prefixed (in later use often parenthetically postfixed) to the particular word, phrase, or clause, on which the extreme character of the statement or supposition depends.
Merriam-Webster says "even" can be "used to stress something that is surprising or unlikely"; it doesn't necessarily have to be surprising, but if it is so, even intensifies that. Also relevant, "used as an intensive to stress an extreme or highly unlikely condition or instance: so simple even a child can do it".
With that said, I think indicating "extremeness" is the operative function of "even"; if there is surprise, it isn't indicated by even, so much as stressed by even.
I think all the sentences you listed are grammatical; however, I don't think any of them necessarily indicate surprise. I'll take the last sentence:
I'll even give you even more[.]
which I do think is workable. The first "even" is an adverb modifying "give". This "even" is emphasizing that what is being given is an "extreme case"; the speaker does not regularly "give more" but is in this case. The second "even", also an adverb, modifies the adjective "more" (as in "more ice cream"). This usage is covered by 9e:
Emphasizing a comparative; ‘still’, ‘yet’.
So, the sentence would be equivalent to saying
I'll even give you yet more.
As for the even at the end of the sentence:
I'll give you more, even.
In this case, I'm pretty sure that the even is simply the even that modifies "give". In other words, this is semantically identical to "I'll even give you more." Moving the adverb to the end of the sentence, however, typically intensifies it. "I'll eventually go home." v/s "I'll go home, eventually." As such, that construction has intensified the intensifier, if you will.
I'll give you more. < I'll even give you more. < I'll give you more, even.
So the second "even" intensifies "more" and can be used with or without the even that intensifies "give". Theoretically, then, "I'll give you even more, even" would work, but it sounds clumsy at best. I suspect that has to do with the intervening adverb in general more than the two evens ("I'll give you still more, even" doesn't sound much better to me). Regardless, I don't think any of these constructions affect the extent to which surprise is indicated, as such. I think that they do affect the intensity, and if surprise follows, then it is affected as well.