Applying black plastic over the top of the soil/root system of the trees is a BAD thing to do to the trees. The entire soil/root system needs to be exposed to air circulation, gas exchange, water percolation...not just where a few holed are cut.

Why can't the ivy be kept in place, but kept off the tree trunk?

When trying to protect and conserve valuable trees, you have to look DOWN, not just up. Do all you can do to prevent that plastic from being laid over those root systems.

Also, demar, you might want to post this same question in the TREE FORUM, where is truly belongs. You'll probably get some other good ideas over there.

Or, the Northwest gardening forum where people understand the problem ivy creates in our climate and know why it's a noxious invasive here :)

Demar, removing the ivy isn't going to be a one time chore, you'll have to keep up with it for at least a couple of years. The recommended steps for removal of ivy climbing trees are - cut at shoulder and ankle high, remove what's in between. Pull/dig as many roots as you can from the ground. Then cover with 6 inches of bark or wood chips, no plastic (keeping bark 3 inches away from contact with trunks)...you can get away with a mulch that deep using the more coarse material that won't pack down.

Since ivy grows year round here in our mild climate, about every 6 months you'll have to give any new sprouts some attention and remove those, apply more mulch, but after the initial cleanup it will be a much smaller job and won't take the same effort.