Yes, it would be better to untighten the big groove nut a little before adjusting.
But, like most of all Strida users, you do not own a 60 mm ring nut key (the big one with three holes shown in the middle), I guess.
Maybe you should email your fellow countryman, Mr. Schlumpf.
http://www.schlumpf.ch/
It might be possible he sells one separately. 
For belt tension adjusting it might be useful to insert a 6mm drift punch into the belt extension bolt bore, like shown below:
