English speakers are used to squashing consonants together (eg. the -dst in midst), even though we also drop letters in so many words (like the b in doubt... well, we've never said the b).
Nothing is dropped in midst, but you can say midst of doubt as "mid stov dout". We slide words together a lot!
Definitely don't say "mitt of doubt" or "mist of doubt". These would be funny errors, even from native speakers.