This 10€ surcharge applies to ALL passes for any trip In or to/fro ITaly-and if no seats are open in the system (which usually does not mean really all seats are taken all the way)-then the rather obvious is; ´places debouts´ in FRench: stand upright.

You can lower it-but not avoid it-to use local SAD train Bolz->Brennero (no take passes, pay normal ticket), change to local OeBB trains on=no extra. You could in theory with an earlier start even catch same train as above and board in Innsbruck.

The Trenitalia services from Bozen  to BRENNER are free for interrail holders. Then as the previous post says change to the ÖBB train there. Just walk up the platform and enjoy the ride to Innsbruck. Pick up the EC train there. I did this many times in May this year and always avoided the supplements incidentally it is 15 euros in first class. To be honest paying extra to go first class is a waste of money on this train! 

Hello! So I just got back and this is my experience.
On my way to Munich I did something similar to what @cdwatkins19 suggested . I took a train from Brenner To Innsbruck, then Innsbruck to Kufstein and last Kufstein to Munich.
On my way back FROM Munich I paid the supplement because I stayed all the time on the EC From Munich to Italy.

Only one thing is still not clear to me, if the second class is fully booked and I pay the supplement for the first class (with a 2nd class interrail) , may I face problems when my ticket gets checked?or I could just explain the situation to the train conductor?

As described earlier this is not an upgrade fee. Your pass is your ticket i.e. 2nd class. If you are lucky you will simply be pointed in the direction of 2nd class, otherwise you will be classed as travelling with an invalid ticket and asked to pay full fare or leave the train.