I took a closer look at the Staff of Mighty Sweeping. Its price is 28,600gp. That's 10,000gp more than a +3 weapon, making the staff likely priced out as a double weapon, with 14,000gp for a +2 and Mighty Sweeping on each end. That would place Mighty Sweeping at 6,000gp as a WSA. Or, if it really was priced for a single end, then the price for just that enchantment would be 20,000gp. I'd be inclined to believe the former is correct, given that the staff was MWed properly as a double weapon already.
I don't quite understand where you get the 14,000gp at. But I think the real problem is that you read "mighty sweeping" as one thing, and it's really two things: "mighty" and "sweeping".
Magic of Faerun, p145
Staff of Mighty Sweeping: This sturdy ash +2 sweeping quarterstaff also grants the wielder the Improved Trip feat.
Magic of Faerun, p141
Sweeping: This property grants a +4 bonus on any Strength checks the wielder makes as part of an attempt to trip an opponent with the weapon. Caster Level: 5th; Prerequisites: Craft Magic Arms and Armor, bull’s strength; Market Price: +1 bonus.
So "+2 sweeping" makes it equivalent to a +3 weapon, which as you point out is 18,000gp. If used on both ends, it would cost double, or 36,000, which is more that what the staff costs. The "mighty" adjective is just fluff that refers to the granted feat (Improved Trip), which seems to cost an extra 10,000. Arms and Equipment guide says extra feats usually cost 5-10K, so that fits right in.
It can be confusing, but I think the book just forgot to double the price for a putting an enchantment on both ends, though it did remember to double it for masterwork quality.