Welcome and congratulations on your new babies! Do you have a screen top on your tank? If so, I would seriously doubt your hygrometer readings. I actually cover approximately 1/2-2/3 of my retf screen tops with Saran Wrap to keep from losing humidity but still give ventilation. Do NOT continue to leave the door cracked, you'd be amazed by how little space they need to escape. If you do not see condensation on the glass or water setting in the decor, it is not too wet. Are you using an analogue or digital hygrometer? Analogues are notorious for being inaccurate. Once a little moisture gets in them, they give consistently high readings. Digital are better, but even they will go bunk if they get sprayed. I don't even measure my humidity anymore but it helps to at first while you figure out what the normal feel and smell is. I would say the biggest cause of baby red eyed tree frog death is probably dehydration from low humidity. You'd be better off keeping it a touch too high rather than too low.
If you do not have a screen top, it is an absolute must. These frogs need ventilation to stay healthy.
For the plants, just go to Home Depot or a store like that and pick out some tropical plants. Take them out of their pots and shake as much dirt off as possible. Then rinse it. Then soak it for a few minutes in a 10% bleach water mix. Then soak the plants again in clean water with extra dechlorinater mixed in. Following those steps will make the plants safe. I've been doing that for years without a problem. The only thing that doesn't work on is moss. I really find live plants necessary for red eyed tree frog health.
For heating, I use a ceramic heat emitter with a thermostat attached. That way, when it is warm enough, it just shuts off and doesn't overheat. In my opinion, that is the absolute best way to keep sensitive red eyes at a stable temperature.
Keep asking any any questions you might have, we're happy to help! If you want to post pictures, you can use a photo hosting site like photobucket or Flickr. Our photo uploader has been stubbornly down for some time now.