Scott, you sent them a message at 8:00 pm CST, that would be 02:00 am CET. Give them a few hours to wake up.
Adina apartments hotel: not the greatest location, but the M3 is only about a 5 minute walk but you will need to take that each time you leave your hotel to get to the center of town and that's not terrible, but not the most convenient either, but a very nice part of town (just occurred to me, they are doing work on the M3 and I am not sure what stations are open).
7 seasons apartments; really physically a great location and central to most things, but on Kiraly utca which is a party street for the young European trust fund hoodlums and that's only an issue on holidays and when school is out, otherwise, pretty okay street.
Mamaison Residence Izabella: a block off Andrassy (the Champs-Élysées of Budapest but better than that French street) on the lower end of the upper half of Andrassy home of beautiful architecture, generally quiet and I would say the only drawback is you will need to ride the M1 metro to get closer in.
But the M1 metro, the oldest underground on the continent of Europe, is almost like an amusement park ride so its not a bad thing (of the three, my choice).
I also know a few of the apartments managed by the firm David sent you to; all in good areas and the quality and size pretty much crosses the spectrum (decent company too).