Good question - I could only come up with two words that have 6 vowels: facetiously, abstemiously; these words have 7 vowels: adventitiously, and sacrilegiously.
Stretch is a 7 letter word with e as the only vowel. Twelfth is another 7 letter words containing only one vowel.
Rhythm The 7-letter word is Rhythms
Rhythms.
oatmeal
Oatmeal?
Some people maintain that's "rhythms." I don't agree.
rainbow
The word "sunrise" has the long I as in kite.
The only 7-letter synonym for peace (the answer to this question) may be harmony. But it does not represent an actual period of time as peace does.
3/7
someone
One such word is elastic.