How can I get my Dwarves to use wheelbarrows to haul building material?

Solution 1:

Make a small second stone stockpile very close to your building site. Set it to take from links only and then link it to your main stone stockpile. Assign several wheelbarrows to the small stockpile so your dwarves haul stones to it faster. Your dwarves should efficiently fill the small stockpile with stones and then inefficiently haul stones from it to your building site. Since it is so close, the inefficient hauling should not effect building time much.

If this isn't fast enough for you, the dfhack mod has an autodump command that will transport any objects designated as dumped to wherever your cursor is. You can use this to place any stone needed right next to your building site.