Yes, round-up will most likely kill your trees. You can make a shield out of stove pipe or sheet metal to keep the RU off the tree, which works pretty well. Not as handy as spraying right over the top though.
I believe poast is approved for most trees (??) but will only kill grasses.
I did not have that great of luck with Princep. It is fairly cheap and easy to apply, but for me it only controlled the foxtail which comes on later in the summer. Perhaps I didnt apply it strong enough or at the right time, but I saw very little control of broadleaves.
Round-up in a good back pack sprayer and a tree shield is the only cheap and effective method I have tried, but you may need to do it twice a year. Dont have the green to spare for Oust.
I was checking out a label for Pramitol E25 (I think thats right?) and it was a ground clearing chemical that was supposed to eliminate all vegitation for 1 year. It stated that it had no control over woody vegitation (trees) so I wonder if that wouldnt be a good answer for a spray over the top season long chemical? Anybody tried it or know what it costs? Something tells me it either wont work or costs $2 million an ounce.
Whatever you do it is worth the effort. The trees I have protected from deer and weed/grass competition have outgrown the others 2:1 and in many cases 4:1.