Also, you have to pay for an escort through the tunnel, and while that's happening, you'll be blocking all traffic in both directions.
The road into and out of Zion to the east isn't exactly motorhome-friendly even if you don't consider the tunnel. It might be better to take the long way around from Bryce--Hwy 20 west to I-15, south to Hwy 9 just north of St. George, thence into the park. Somewhat longer, but probably much easier.
If it's March or later in the year, you (and any other vehicles) may not even be admitted into the park, due to very limited parking (unless you have a campground reservation). You'd have to park in Hurricane and take the shuttle bus in. You also have to use the shuttle bus to visit the northern parts of the park road (Virgin Narrows, etc.) after March 1.