This is exactly the bit which doesn't work for me!
Riding on the tops of drops is OK for just lazing along looking over the hedge (this is something I do).
But if I want to make a bit of progress I need more reach; I think what I'm doing is bracing my lower back/pelvis against the muscular effort of pushing the pedal down. On the odd occasion where I'm really trying I find myself "working the bars" and using the cleats to push the pedal over the top and pull it back at the bottom. (I only pull up on the cleats when out of the saddle, and thats really pulling back and up)
I have had a couple of MTBs with flat bars which put my hands at about the "tops of drops" position; I always put bar ends on which gave me a substitute "hoods" position. I would then ride these bikes mainly on the bar ends, which is fine unless you want the brakes in a hurry. Eventually (having gone the wrong way for the brakes a couple of times) I went back to drops for roughstuff. It was too exciting!
Now arthritic thumbs prevent me using drops, because I can't hang off the hoods on my thumbs to brake. (I also can't hold conventional flat bars for very long....I can ride resting the heel of my hands on the grips, but braking is interesting)
I think with my bullbars I'm using about the same stem lengths as I did with drops (Nitto noodles, with the long ramps) So the back of the grip substitutes the "tops" position, then I have a long grip which substitutes ramps and hoods position. I don't have the drops of course, but I can get down a bit by holding the very front of the bar by the brake levers.
Saddle nose to bar boss is about 52cm; then I have about 12cm of grip plus the bit of bar the brake lever mounts to.
As you say, the Longitude is a long bike, it wears a short stem....
IMG_5332 by 531colin, on Flickr
(its changed a bit since then)
Despite the long top tube, I still have bullbars with grips going forward from the bar boss. I couldn't make the grips come back towards me, it would require an un-feasibly long stem.