How to spell the contraction of "might as well"

Solution 1:

It sounds to me like you are mis-hearing "may as well" and interpreting it as "might as well -

We can use may as well and might as well for making suggestions. We can use them to say what we think is the easiest or most logical course of action when we cannot see a better alternative. They are both fairly informal. Might as well is more common than may as well

dictionary.cambridge.org

When these words are said quickly and rolled together it is easy to see how they might be heard as "mares well", in my opinion.

Solution 2:

I once saw this contraction written as part of character dialogue - I.e. to display the character’s dialect - as ‘Moswell’, ‘Mosswell’, or something very similar. I will invent an example.

“I say, Erik, the scouts are reporting an enemy camp setting up near the river, about six miles west.” Erik considered this new information for all of five seconds before he grunted, stood up, and hefted his war-axe. “Moswell go over and give ‘em a kickin’ then, eh?”

I would suggest that in American English the verbal contraction of ‘may as well’ becomes ‘Mayswell’, where as ‘might as well’ is barely contracted - it’s just said quickly and sounds like ‘Midaswell’. In British English, the contraction is still ‘Mayswell’, although some dialects, particularly northern, definitely have a vowel pronunciation that sounds closer to ‘Mehswell’. In British English, the R in the word ‘Mare’ is rarely pronounced. Imagine pronouncing ‘Air’ without the R sound at the end, and you’ve got it. ‘Maiswell?’ In British English, ‘might as well’ becomes ‘my’aswell’, with the apostrophe after the Y signifying the staccato stop where the T would normally go. It is simply missing.