It can be done.
First, you should take a train from Perm 2 station to Nizhny Tagil ( http://pass.rzd.ru/main-pass/public/en ). The train departs from Perm 2 station at 10:33 (attention please, this is Moscow and not local time) and arrives in Nizhny Tagil at 19:25 (attention please again, this is Moscow and not local time). When looking for this train, keep in mind that Nizhny Tagil is spelled on the search engine on the mentioned site like Nijnii Tagil. This train, called Malachite (Малахит in Russian) runs on Mondays, Wednesdays, Thursdays, Fridays and Sundays, so that you can plan your trip.
As you can see, Nizhny Tagil is north of Chelyabinsk and Yekaterinburg, so you will feel quite comfortable.
Second, take a local train from Nizhny Tagil to Egorshino. There is one daily train on this route with departure at 05:15 (again, attention, Moscow time, not the local one). Egorshino arrival at 10:13 (Moscow time).
Third, take a daily train from Egorshino at 23:35 to Tavda. It arrives in Tavda at 05:23. Again, Moscow time.
Fourth, take a bus from Tavda to Tyumen. There are several daily buses (http://russticket.com/ ), so you will choose one. The ride between the two places takes between 2:40 to 3:15 hourse...
As you can see, the closest place on this route to the route you want to bypass is Egorshino, but I assume this is far away enough to be on the safe side and feel comfortable. Also, I am aware that this route is a bit exhausting, but it is without any doubt doable.
So, it's up to you to decide.
