Now you have everything you need to schedule the meetings and make them appear correctly for everyone involved: The date and time of the meeting, the timezone of the meeting, whether or not DST is occurring there at that date and time. Store everything in the database separately, and store all datetimes at UTC.
This is the solution I built once for an "enterprise" client†, and it worked pretty well.
† a global lawfirm, who regularly needs to schedule meetings across timezones.