Yes, it is grammatically correct. "what"= direct object of verb "should" "what" replaces "sound like." Original: ... than what we think we should ... Equivalent: ... than we think we should sound like ... "it" = subject of verb "doesn't meet" "it" replaces "the fact that we sound more high-pitched." Original: .... as it doesn't meet our internal expectations. Equivalent: ... as the fact that we sound more high-pitched doesn't meet our internal expectations. or ... as sounding high-pitched doesn't meet our internal expectations.

Why don't,t you try it and I'll correct it.

Not technically speaking grammatically correct, no. 'What' should be omitted. The sentence should be clarified, and cut into two shorter parts. 'It' refers to the sound of 'our' speaking.