In North American English, the vowel in got isn't pronounced [o], as in hope. It's pronounced [a] as in father. Like this, g[a]t, and it rhymes with "hot".
This is how got is pronounced in your example sentence,
Ex: I g[a]'[D]uh meeting tomorrow.
Hopefully someone will come along with an IPA version.
All the best.
this has to do with the aspect (in connected speech) called assimilation and in this case the voiceless /t/ is voiced, becoming a kind of /d/ and this often happens when /t/ (voiceless) is surrounded by voiced sounds in a single, two-syllable word . Ex: matter, butter, dirty,etc.
but when we pronounce for example: I got to go, isn't an /r/ sound heard instead of /d/ ?