Zinsser Perma White is a semi gloss almost the same sheen as an eggshell paint, 2 or 3 coats and that's it with either paint you decide to use. Forget Matt paint in your situation unless using Crown Extreme Matt.
So just scrape on the peeling paint & paint on 2 coats of Zinsser, no need to apply anything else like a mist coat? Which Zinsser finish to buy is what I'm asking as on the tin it says matt?
After scraping, filling and sanding thin the first coat with about 20% water added, when dry (may be best to leave overnight) sand any knibbs off and paint on the 2nd coat...when that's dry apply a 3rd coat...... should be looking the bee's knee's once dried out.
And the Zinsser paint what finish should it say on the tin as I only seem to be able to find matt or satin?