I can't go that far. What country are you from? I would have said the second syllable of "refrigerator", and the first syllable of "Frigidaire", both obligatorily rhyme with "ridge". There's no alternative.
"Frigidaire" should only really differ from "frigid air" in terms of prosody.
California. I suppose it's just a difference in accent, because I've always heard Frigid pronounced somewhat like fri-jid, with a clear enunciation between the parts, rather than the blended "dg" sound.
I'm actually assuming it pronounced with a more enunciated J sound than other poster accents seem to. I've always heard frigid with the emphasis on the "J" sound, rather than the softer blended j sound that produces the "dg" blend.
"Frigidaire" should only really differ from "frigid air" in terms of prosody.