never mind sitting on a chair back wards, why not get a chair that is designed well with a supporting back that slopes very slightly backwards and then be conscious of posture.
next try opening and closing the hands this will make the performer yawn, which helps singing. take advice from classical singers who know how to use their voice and look after their voice, but whilst singing correctly, avoid a classical opera style that involves using excessive vibrato.
this kind of chair
http://www.skibbereenmarket.com/images/charleyschairs2.jpghttp://www.skibbereenmarket.com/images/charleyschairs2.jpg