I would definitely continue with the carrot rewards, it's just a bit of fun and then both of you get something out of it :) I always try to teach 'tricks' like these without any pressure or manipulation because the horse can really figure it out for himself and you can take your time.
I think of a bow as having 3 different components which you can shape individually and then put together slowly. I would advise you to start from scratch and don't just try to alter the bow you have now. It might confuse him because he thinks he's doing it right already ;)
Firstly I shape a leg lift which I teach using a foot target so I don't need to pick up the foot - but you could just as easily teach it by lifting his leg if it's something he already understands the cue for. Give him a treat for holding even the smallest bit of weight on his own. Keep gradually building on that until he is picking up his own foot and holding it in the air for a few seconds. That's the key part for him because it's the one bit he doesn't already know.
Then I would encourage a leaning backward motion by using a target but this can be done using a carrot lure under the chin and through the legs (which it sounds like you have done before so he should grasp that quickly) Eventually you can lure the head down in the same way.
Duration is a really tricky part of trick training because you have to make staying in that position really rewarding for the horse. The only way to do that is to give lots of treats all the while he is making the effort and VERY gradually raise your criteria for more time. It will be very slow progress but just remember all the while he is offering something closer and closer to what you want you have to reward him. You should be asking for more in very small increments. That way he learns that there is always something more to be working toward to get more carrot! but it's not so overwhelming that he gets confused :)