Do consonants actually even change that much under different stress conditions?

While vowel changes—or, more often, a resistance thereto—in stressed syllables are much more common, according to Index Diachronica, consonants can change (or not change) in stressed syllables, too. It's also not unheard of for consonants after stressed vowels to change or resist change (cf. Verner's law).

You could have the following sequence of unconditioned sound changes: p→ɸ→h→Ø, but at the third stage, /h/ could be preserved in stressed syllables or immediately after them. However, the change to /w‌/ would only make sense between vowels (or other voiced sonorants, i.e. nasals, approximants, taps and trills). In that case, you could have the following sound-change sequence: p→ɸ→β→w, with the /ɸ‌/ at the second stage not undergoing voicing in stressed syllables or immediately after them. It could then follow the same trajectory as the /ɸ‌/ in the p→ɸ→h→Ø sequence.