Michael,
Welcome to the site.
I think this issue deserves some research to find out what size to tap the holes to! M6 means 6 mm, which is .236," but thread names don't exactly match thread sizes. That is, the top and bottom of a thread can't both be, for instance, 6 mm. Let's say the top of the thread is 6 mm. That means the hole it goes into must be less that 6 mm, because the thread has to stick out far enough to get to the bottom of the screw thread.

Anyway, I'd play around with different screw sizes near that... since 1/4" is definitely larger, I'd probably try tapping it with that. And since the thread pitch is either 25.4 threads per inch (1 mm pitch) or about 34 threads per inch (.75 mm pitch), I'd go for the thread furthest from what's been cut. That would be 1/4-20 instead of 1/4-28.

Measure how much of that hole is threaded, and if it seems like it will work, decide for yourself what you're going to do; get a tap made for a blind hole; get some oil; and tap that! Hell, I'd tap it!