For referring to the actual past here (albeit one that did not in fact transpire - so "actual" would probably be a better way of putting it!) you'd need to change the 'went' to 'had gone'. [Obviously the modal 'would' + 'base form of verb' is generally less confusing (in that modals aren't, with regards to their form/formal classification, so much tensed as simply just 'finite'), but trying the same switch to "actual" past on 'would go' (with the addition of 'have' and a change of 'go' to 'gone': ?
I wish she would've gone out with me) would be as unnecessarily wordy (cf.
I wish she had gone out with me) as using 'would have' rather than just 'had' in the protasis (=subordinate, if-clause) of a conditional sentence:
http://tinyurl.com/3952zaa (a link to a relevant entry in the Google Books full preview of
Merriam-Webster's Dictionary of English Usage)].
Or you could change the wording so that the 'went' becomes literal:
"I wish that the statement 'She went out with me' was/were true!".
But getting serious again, I suppose that the (whatever, any?) "volitional" aspect lurking in 'would' can be better distinguished if and when given extra-explicit and "helpful" i.e. matching versus mismatching context within contrasting examples (see those below, and note the would-won't symmetry in the first), but the second of
your sentences certainly isn't
incorrect, DGD! (As SJ before me also confirmed, albeit
very succinctly!
).
I wish she would/she'd go out with me, but she won't.
?
I wish she went out with me, but she won't.
Does 'went' sound as acceptable when the tense of 'wish' is actually itself past, though? Probably not!
I wished she would/she'd go out with me (but she wouldn't [=back then, obviously!]/but she won't [even now]).
??
I wished she went out with me (but she wouldn't [=back then]/but she won't [=even now]).