Hypericum? I wouldn't expect roses or any other flower to "squeeze" --- more likely that the St. Johns wort would be the winner in that battle because it has had time to become well-established.

Black plastic will eventually kill anything under it, provided no light ever gets through (it's the lack of light, not the plastic that does the killing).

You don't say what you want in place of the Hypericum.

I'd recommend a form of lasagna; if you're careful to lift and lay down small amounts of material at a time, making lasagna shouldn't be stressful to your back. The key is the first -or bottom- layer. You want it thick enough to last for a while. Cut or mow the present plants [leave the mowings]. Then pile up wet newspaper until it's about 1/2" high --- this is a LOT of newspaper. If you just want a mulched area, top the bottom newspaper with 3" of organic mulch such as shredded leaves. This should kill the hypericum. The mulch will have to be replaced -or added to- annually unless you use wood chips which will last a couple years. If you want a real lasagna, then make layers on top, alternating brown [dried] stuff and green [grass, kitchn scraps, etc] stuff with 3 or 4 sheets of newspaper between each layer. Go over to the "New to Gardening" forum and search for 'lasagna' to get more details.