You can go higher by pushing yourself up on the upslope or popping off the lip. Nobody is disputing that. In a halfpipe you can do this over and over to build momentum because the curve of the wall converts the vertical movement to horizontal movement when you come back down the wall.
You cannot gain speed horizontally on an up-transition by only doing this. Swinging your arms from front to back in the direction of travel would give you a boost, but you'll lose the speed when you swing them forward again. On a series of large jumps you can add vertical momentum to a point and recover it, but eventually it will make you miss the landing. On small bumps (like the size of ski moguls) you're limited in when you can do this because there is very little margin in terms of good landing points. Either you have to not jump at all (by absorbing the uphill more as you go faster), or you jump far enough to skip an entire bump. So it's very hard to gradually build speed using that technique.
I tell you what. Since it is apparently so easy to do this, I'll PayPal $50 to the first person to post a video showing someone gaining horizontal speed on an up-transition like this one:
solely by 'pumping' (ie, flexing or extending to reduce/increase pressure, like a skater in a halfpipe) on their conveyance while going totally straight. It can be a skateboard, inline skates, bike, unicycle, skate skis, whatever. The transition can be curved if you think that's necessary or helpful, as long as it's 'uphill' the whole way.
The goal is to be going faster (to the right in this diagram) at point 3 than at point 1. The speed gain needs to be significant (let's say at least 1 m/s) and measurable (so either shoot in profile like that diagram or put chalk/tape marks on the ground at regular intervals that can be seen in the video). It would be preferable if you did it twice in opposing directions to show it's not due to the ground being sloped or the wind pushing you or something.
Some rules: No turning, and you have to be square to the ramp (like in that 2D diagram). You must be freely rolling the whole time; no flipping yourself over the front of your bike by jamming the front brakes or anything like that. Jumping is okay as long as you do it just by extending and flexing your legs; you may be able to throw your weight around and bunny-hop a bike to gain a little speed, but that's obviously not what's being discussed here. No swinging body parts backwards; you must be in the same body position at point 3 as you were in point 1.
Easy money the next time you're at the skate or bike park, amirite?
You forgot to disallow sideways pumping (in and out of the plane in which the text is written). Just say'n.