we went to Moab end of May and based on all the information we received we did decide not to do the whole WRT.
We entered the WRT in Canyonlands NP and went down the Shafer switchbacks until we reached Musselman Arch (great!). There we returned and went back via Potash Road. Shortly after reaching Potash there is another dirt road (Long Canyon Road) leading back up to the entrance of Dead Horse State Park. We tried this road but with our 4x4 Jeep Liberty without Low transmission we could not get through a short area with deep fluffy sand almost at the end. So we decided to return to Moab from there and call it a day.
It was a wonderful day trip and in current conditions the WRT (the part we did) is not challenging for a 4x4 HC vehicle.
Thanks for all the tips!