Triclopyr has been my choice for woody plant control for 15 years. It works great on poison ivy. However, poison ivy has surface and underground stems, and the chemical is often not completely translocated thru the whole system of vines in enough quantity for a complete kill. I have seen an area cleared of poison ivy for 2 years where a new sprout suddenly appears. Careful digging of this plant reveals that it is coming from an old root or piece of stem.
I have one bed of English ivy where I have been working on the poison ivy for 4 years. Used mostly a wicking application to preserve the desireable plants. First year also removed a 1" diameter stem growing up the house - this stuff was WELL established. Few plants around in 2nd year. Nothing 3rd year, but have a few popping up this year.
If you are doing a complete redo of the area, I would do a complete kill now, mulch to control new weed growth, and wait 12 months to get any poison ivy stragglers. If it is well established on this site, and for some reason you do not get good control in initial app, your tilling will likely create numerous viable pieces to sprout anew.