Monroe early rifle tag is a long ways out. You aren't drawing that tag for 13+ years. Even the muzzy tag on the Monroe is not guaranteed at 19 points.
Not many places on earth that you can ride the roads and have a great chance at a good bull. It happens, it just takes more luck than anything. I would not want to leave 19 points and a one time opportunity on a mentor tag for your daughter to luck. I would want to stack the odds in my favor as much as possible. I totally understand the situation, though.
I would look hard at the Manti. There are a ton of elk, so going around and getting excited about seeing elk would add to the overall experience. There is a real good chance at a 310-320 type bull, with a decent shot at one much bigger. There are a lot of roads to get places, but as stated above, you're going to have to walk a little bit at least to give her a chance at the bigger elk. 19 points is beyond what it takes to draw, so you'd be guaranteed. But if you are looking for a unit with a lot of elk to see, good access, and a chance at a mature bull, I think the Manti fits the bill. Of course, the roads are usually up high and drop down into the pits of hell, so once you see one or after you shoot one, you'll have your work cut out for you. But it's a great unit.