Your Merriam Webster source has "val-it" as the first pronunciation (but I think in this case both are correct and valit is less common)
It does.. and I've never heard anyone say it that way (and I appreciate that you chose the only dictionary that gave anything close to your argument).. but that's still nothing like "ballot".
Drink some clarit with the valit over a good filit.
Jeeves (the gentleman's personal gentleman) is a valet that would be pronounced VAL-et.