Many poets will tell you that the near rhymes, if any, should come earlier rather than later in the poem, so it doesn't seem that you have resorted to near rhymes only because you have run out of perfect rhymes. By using perfect rhymes after your near ones, it reassures the reader that the near rhymes were a purposeful choice and not just a compromise because you ran out of steam.
Personally, the question of near rhymes strikes me as twofold, (1) is it acceptable as poetry, and (2) is it acceptable to editors, many of whom may not be that educated about poetry or confident about their own ears, and so they resort to rigid rules that don't necessarily make sense.
There are too many examples of famous poems, in children's and adult literature both, that employ near rhymes for anyone who knows anything about poetry to stand by a blanket rule against near rhymes. It merely betrays ignorance.
But near rhymes are something it's easy to complain about in a poem that may otherwise be bad for reasons that are more difficult to articulate, and so they are often singled out for unfair criticism.
That said, I rarely use near rhymes and prefer perfect rhymes in my own work.