* fast track /fæst træk/
* swim meet /swɪm mit/
* Fat Tuesday /fæt tuzdeɪ/
* hat trick /hæt trɪk/
* fake coin /feɪk kɔɪn/
* drip pan /drɪp pæn/
BTW, I don't know if your account of how the phonetics of such words works out is correct. The traditional account is that in situations like this where the same consonant appears on either side of a word boundary, English speakers actually hold the consonant for a "double length", which is called gemination. (This is in fact very common in some languages, such as Italian, e.g. "sette" 'seven' vs. "sete" 'thirst', but English only recognizes consonantal length contrasts in consonants in this limited sort of situation.) The Wikipedia page has a good discussion: https://en.wikipedia.org/wiki/Gemination#English
You can verify this for yourself by comparing some minimal pairs. Consider:
1a. fast track /fæst træk/
1b. fast rack /fæst træk/
2a. fake coil /feɪk kɔɪl/
2b. fake oil /feɪk ɔɪl/
In my personal English, each a-b pair differs only in the amount of time I produce the /t/ or /k/ closure for at my alveolar ridge or velum.