If your system was actually engineered each zone took into account the r value of the floor (which resists heat transfer), the area of the room, the height of the room (there by volume and load) and the R value of insulation of the room and the E value of the windows and doors (heat loss).
If you change significantly that zone will struggle. You want waffle or solid rubber padding for carpets with LOW R value. check www.sponge-cushion.com
re-bond pad will work also if the budget is tighter. The carpet itself has r-value. The carpet stores wont usually know this... there is a ballpark figure like r/sq inch just google it.
wood floors can be used. Engineered wood moves less so is a safer bet, Skinnier planks are better than wide and you want to check the temp that zone is designed to run at... I think maybe 80 or 90 degrees is the max you want to run under wood.
My entire house system runs at these temps, even with carpet... but I used aluminum heat transfer plates and a lot of tubing to do this. I have seem systems running practically boiling water at the start with one long run LOL, half the house you couldnt stand on the tile and the other have was freezing. People shortcut the engineering and think "I have hydronic heating." It is nice when it's right, I love ours, but I'd take good old baseboard anyday over an improperly designed radiant system.