The key to buying cheap aquarium tweezers online is to leave out the search term "aquarium". That pretty much always adds a premium to anything, including foam, semi-aquatic plants, pumps, lights, etc.
At least that used to be the case. Just looked on amazon: aquascaping tools have come way down recently! You've got no excuse: get some forceps!
As for carpeting, I find most plants learn to keep their heads down to the substrate if you brutally chop at them with scissors. Same for mosses. Monte carlo also looks good crawling on the ground as a big bushy, jungly carpet, so you might also decide to just let it go. How old is this tank?