Valet: pr val’it (and conversely Dr Bill, would you ever hear of a car vallaying service? – certainly not on this side of the pond I think!)

Fillet: pr fill’it (as already noted, a fish would never be described as other than fill’it’id)

I disagree on all counts.

I say val-lay, and it's a val-lay service, no -ing about it.
I say fil-lay, and a fish upon whom said operation has been carried out has been fil-lay'd. But I'd be in a bit of a fix if I had to actually spell that last one, in the formal writing-stuff-down-on-paper sense.

I'm from New England, but live in California, and I have even pronounced it this way when I've been in other countries, so this pronunciation must apply there too.