I was wondering how you pronounce "that that", as in: "I'm sad that that man won't come with us." I pronounce it "ðət ðæt", but I'm not sure if you'd pronounce it with two schwas or æs.
Yes, I would reduce the vowel of the first that too, normally. However, I don't rule out the two thats with full vowels or with reduced vowels. (Well, I tried saying those versions to myself, and they sound OK. The double full vowel version sounds a bit ponderous, and the double reduced vowel version sounds more likely.)