Have you tried breast compressions too? He may be less likely to fall asleep if he's getting massive gulps of milk. Google youtube Dr Jack Newman breast compression and there is some information here on sleepy babies
Strip him off beforehand, he won't feel so cosy then and won't be too cold against you provided your house doesn't fall to subzero temperatures at night. Also press and squeeze the palm of his hand, this helps stimulate them and wake them up. Alternatively flick the soles of his feet, although do that gently as he might not like that.
Has anyone got any suggestions as to how I can discourage my 5 week old lb from falling asleep 5 minutes after I've started breast feeding him during the night? I struggle to wake him to carry on once he's fallen to sleep, and I think he's only sleeping for an hour at a time because he's not full enough.