I'm not sure why the asker didn't find many many references online to this issue. The OU, for example, says this:
- The Shulchan Aruch (YD 95:1-2) rules that if a pareve food was cooked in a totally clean dairy vessel, the food may be eaten with meat, and that if a pareve food was cooked in a totally clean meat vessel, the food may be eaten with dairy. The Rema argues and rules that pareve food cooked in a dairy ben yomo (i.e. used with hot dairy in the past 24 hours) vessel may not be eaten with meat, and vice versa, but that b’dieved, if such foods were mixed together, they may be eaten. (Thus, according to the Shulchan Aruch, pareve soup cooked in a totally clean dairy pot could be eaten with meat, whereas the Rema would prohibit it.)
I'm sure a thorough search would find plenty of detailed citations for other halakhic commentaries. There are also a number of "Ask the Rabbi" sites, and it seems to me that in this case the Ashkinazic rabbis are familiar with the Sephardic halakha.
The short answer (with the caveat of course that I am not a poseq) is that a truly pareve item cooked in dairy equipment can be eaten with meat by Sephardim lekhathila and by Ashkenazim bede'abad; while it can be eaten immediately after meat by everyone lekhathila.