while having a designated trader is important in the beginning... it becomes less so when you produce so many goods that you have excess. AFTER buying out a caravan.
One tactic, in a pinch, as noted is to set anyone to trade... do so only to get precisely what it is you need in that pinch (metal, food, booze, fey mood request, etc.)... then set trade back to broker only. Consider it a happy medium.
In any event, some things like wood, stone/bauxite, most food and booze are relatively cheap. I recommend doing several small trades rather than one big one:
1) improves negiotiation skill
2) makes it more unlikely that the trader thinks you are yanking him around causing him to
3) leave and prevent you from getting at least some of what you need.
As for meeting with liasons... I dunno, my mayor is a miner/engraver/etc ... I turn off everything but healthcare and tell him to trade... after I stop request for trader, he usually runs back inside to conduct meeting (occasionally runs right back out to grab food/drink).
What i suggest is, set a small food and drink stockpile in your mayor/meetingperson's residence... when he gets there, lock the door. Preferably with the liason inside with them, but otherwise, they just talk through the door and it's not a problem. Prevents your mayor from running about willy nilly doing random tasks, but hopefully also prevents dehydration and starvation (make sure you have a small stock of food and booze, and not just one or the other; hunting for vermin cancels everything).
warning #1: don't forget to unlock the door =p
warning #2: do NOT unlock the door until the AFTER the liason starts to leave... there is about a 2-5 second pause after the final dialogue screen before the meeting actually ends. If you open the door too early, your mayor might start running amok and prevent the meeting from ending... not good.