As long as you carefulle remove that Tyvek suit after pulling those plants and throw the suit away. Because there is some evidence that the urushiol can stay in your clothes washer any clothing worn when pulling this stuff should be tossed out and not washed, especially in a machine clothing of other family members will also be washed in.
Glyphosate products have not been very successful in controlling Poison Ivy, Oak, or Sumac, and usually spending money on these products is a waste.

I think that the tyvec will work, too. You know that you can't burn the brush, right?

Oh yeah, I do. You're supposed to bag it up & throw it in the trash - but what happens then? Doesn't it get burned when it goes to the landfill? I wonder if I bagged it and just let it die in the bags, how many years it would be before the urushiol wouldn't be a problem any more.

I pointed out to this landscape guy who wanted to use Roundup that nothing would grow there if he did, and he looked at me like I had three heads, saying, "Yeah, you don't want it to grow back". But, like maybe I'd like to plant something else there that WOULD grow?

As a normal practice anything you send to a landfill is not burned, it is buried. However, on rare occassion a landfill may catch fire since this buried waste does produce methane gas which is very flammable.
That said in many places sending yard waste to a normal landfill is forbidden (in Michigan a state law prohibits this) so yard waste is supposed to be sent to a seperate landfill often where it is composted.