Trouble thicknessing cypress

I'm trying to thickness a board of italian cypress that I'll use for a uke back, but I'm having problems either with the Wagner Safe-T planer (not the original one, but I used it with other woods without problems) and planing by hand.
This wood is beautiful, has a great perfume and a bell like tone when tapped, but rips a lot.
I tried to re-sharpen both the Wagner and the hand plane, which I knew were already sharp, just to be sure, and nothing changed. With the Wagner I almost burned the piece of wood because it was very hard to make the wood scroll under the bit. By hand I can only make a very fine shave and use the plane perpendicular to the grain in order not to rip grain, so it looks like it will take forever to thickness this. I don't have a drum sander so, any suggestion? Do I make something wrong?
I already made the same operation on a couple of boards made out of different woods and I had no problem, but I'm a beginner, so it's likely that I'm missing something.
Btw the plane is a Veritas Apron Plane, the only one I have for now, is this the problem? Maybe I can solve the problem using an higher angle plane?

Pete Howlett before he had a drum sander... used to sand in the drillpress using a device similar to the Safe T planer, only it had some 60 grit abrasive paper glued to it instead of cutters..I remember he had a 1" dia hole in the centre of the sanding disc to avoid trailing marks..He must have built a stack of ukes this way..If he reads this..Maybe he can chip in and tell us more about it
I found this on Youtube(More or less the same idea)
http://www.youtube.com/watch?v=l98KobHZ0rk and this one http://www.youtube.com/watch?v=kppvo1YR0Wc

I think a bigger plane will be better. I like my Veritas Apron plane but you must be aware of its limitations. I recently changed the angle on one of my old Stanley planes, a number 130. It's not possible to raise the blade (as on some Lie-Nielsen planes) so I just ground the edge differently. And it was a big difference, now it planes difficult wood easily.

How thick is the board?

Didn't think about the sanding disc, thanks Timbuck! I think I'll try to make one, since it looks also quite simple to do.
I was already planning to buy some other plane since the apron plane is great but I already realised it's not the best choice for everything, even if it served well as a multipurpose tool for my first steps in the lutherie.
The board is now 3,5 mm, I've managed to bring it to that thickness with a lot of hard work with the apron plane, working only perpendicular to the grain, it's original thickness was 5 mm. The work's going well, so the only problem seems to be the time and energy I'm consuming to achieve the result. I'll have to thickness the sides also after this board, and I want to come to a good solution for the next ukes..

A scary fast way to debulk timber is to use a sanding disc attached to an angle grinder.
Very easy to go too far though. I hear they even make sanding disks finer than 40 grit too

I thicknessed my first guitar back top and sides with a hand held belt sander. Run it at a 45 degree angle to the grain, keep it moving and measure a lot. You can go as fast or slow as you wish. Do it on a flat surface and don't let the sander roll onto its side. The poor man's thickness sander.

I will punt to all the real experts, but I when I bought a drum sander I promised myself that I wouldn't use it as an excuse for not mastering a plane (which also meant that I'd have to finally get something really sharp at the right angle). I was fortunate enough to get some help from Brian Burns (www.lessonsinlutherie.com). He uses only block planes on his classical and flamenco guitars. It worked for me 100%. He's also very gracious and available by phone.

I don't know what Pete was using; however it sounds very similar to the sanding disc setup that Brian uses which he learned from John Gilbert (classical guitars). If you have interest, I'll ask Brian if I can post his pdf's...however, better for you to make contact with him directly. He is a remarkable resource.

P.S. His double bevel sharpening manual ($12-14.00) has a great explanation of high/low angle planes uses and cutting angles for everything from douglas fir, figured maple, Brazilian rosewood and even aluminum. Also contains plans for everything. A bargain!

Veritas Apron plane is a low angle bevel up Plane. Almost certain to cause tear out on difficult wood. Planing across the grain though is the correct approach.
It's hardly the ideal Plane for such a task. When thicknessing Backs, Tops and Sides I will employ 3 different types of planes - or Planes that are set up a little differently. The first is what I call a 'gentle' scrub Plane. Not a scrub plane as such but it has a blade that is fairly heavily cambered. Wide mouth. This is used mainly across the grain and removes material fast. You can use a No.4 for this. I use an old wooden plane. This is followed by a Plane that is set to take a much finer shaving, less cambered blade. It removes the roughness of the scrub and does the near final thicknessing. Again mine is a wooden Plane. Finally comes the super smoother. Very tight mouth, cap iron set very close to the blade edge. The shavings are so fine that you almost think they will float. It should leave such a fine surface that 600G sandpaper would ruin it. Only on difficult/highly figured woods or Tops with bad run out should you ever need the scraper.

Thank you all for your precious help.
So, it seems the angle grinder and hand held belt sander methods work for someone, but I think I would probably ruin wood and never be able to achieve a good result. If I have to use power tools I want them to be fixed or drill press mounted. I'll look for some old n. 4 on ebay and try to make the sanding disc. Then I only have to master my hand skills.

I have not worked with the wood you describe, so take the following with that understanding.

You can use a router with a flat cutting bit to thickness and surface wood. Basically, you set up a set of rails that bridge the wood and provide a level surface. I'm sure youtube is littered with variations of this idea. I've used it to surface items tha would not fit in my planer.

For dealing in tough to plane woods, look at a toothing (?) plane. It is a steep angle plane with blade that has a bunch of grooves leaving the edge like a bunch of chisels. You plane to just over you thickness and then plane to remove all the little ridges.

Let me know if you want further info on these.