I just learned about slant rhyming where you use a distorted not quite rhyme. Emily Dickinson is noted or these. (I personally don't like these, as they distract. Much like trying to make a pun on Polish the nationality and polish to make shiny just because they are spelled the same way.)
But on the flip side, here are a few that go the other way. Forcing the rhyme to work by changing the word.
Ogden Nash:
Parsley is garsley
Bennett Cerf and the extended abbreviation.
There was a young lady from Del.
Who was most undoubtedly wel.
That to dress for a masque
Wasn't much of a tasque,
But she cried, 'What on earth will my fel.?'
Or you can just mangle the spelling to enforce the rhyme.
In New Orleans there dwelled a young Creole
Who when asked if her hair was all reole
Replied with a shrug
'Just give it a tug
And decide by the way that I squeole.'
What is this called?
Edit: A commenter asked if another answer fit. I said "The question there is very similar to mine, although the example is hard for me to parse as it's structure is odd. The answer is mostly slant rhyme lacking, the cleverness that the examples above have."
In the extended abbreviations example, Cerf does a fun wordplay. The abbreviations make the limerick scan correctly, but if you don't expand them the meaning doesn't make sense. And the other two expansions don't work as real words, but spoken aloud make perfect sense.
'Masque' is rhymed with 'tasque'. This is visual word play. Spoken it could just as well be mask and task. By using 'tasque', Cerf is adding a visual word play.
In the next one, the author uses exact rhyming spelling, but to make the rhyme subtly shifts the pronunciation. 'Reole' wouldn't be pronounced the same as 'real' but more like 'ree owl' where 'owl' is like 'bowl'. Similarly with 'squeole'.
Where slant rhyming comes across as being lazy and sloppy, this sort of thing is a humourous and clever form of wordplay.