Stability difference up vs. down wind

I was paddling yesterday and was thinking about the difficulty I experience when paddling upwind.
I have a very unstable boat which I love when going downwind. When I go with the wind I feel very stable and I can paddle hard and lean and have loads of fun. When I paddle upwind however I have lots of difficulty especially when the nose of the boat comes out of the water when going over waves. Yesterday I discovered that it helped if I leaned forward a little more to get my upper body more above my point of rotation but I still needed to do a little brace every 5 strokes or so.
A friend suggested that I might be making my stroke too long and that a higher stroke rate would help.
I will give that a try next time I'm out but I thought I'd just ask your opinion on the matter.
Any tips?

For me, the #1 thing you can do to aid stability (in any conditions but particularly when going upwind or crosswind) is timing your stroke so that at the moment the wave passes under you, you time your stroke with the wave peak. This way, the natural instability that is created by sitting on the peak is counteracted by the stroke brace (having the 3rd point of contact with the water to create stability). If your paddle is in the air as the wave passes under, you will experience a lot of instability. You know the old saying KIPITW! (Keep A Paddle In The Water!). The worse the conditions are, the more important it is to keep paddling!

The advice of your friend is very good as well. Keeping the paddle in the water past your hip will create significant instability. Make sure to keep your stroke forward - from your toes to your hip and not a micron behind it (although in reality we get lazy and do it, if you are unstable pay particular attention to how far back your stroke comes)

Last, you must master the Stroke Brace. That is, turning a stroke into a brace. 90%+ of the energy is still forward propulsion, but maybe you twist the blade or draw inward at the end of the stroke to provide some stability or readjust your center of gravity. When it is really chaotic out (like more than 3 directions of swell / washing mahcine) almost every stroke is also a brace. Applying forward energy while at the same time stroke bracing is key to paddling rough conditions. 

Is this in the SEI or 560? The 560 has a stability 2 rating from Nelo which is only marginally better than an olympic K1 which just sounds miserable in anything but flat water.  Although I dont think Stellar's or Nelo's surf particularly well, the SEI would be much better in waves if you're at all unstable. 

It is the Nelo that is giving me trouble yes. Unsurprisingly but I love the way it surfs. I use the Stellar without problems in  rough conditions but I get so much joy out of surfing the nelo that I would like to be able to use it more.

The Nelo is fairly short, in my 550 I can affect a lot by leaning forward or backwards when heading into waves (assuming they're of decent size). Sometimes I prefer to lean forward and punch a bit more through the wave as opposed to going up and slapping down, etc. I assume the 560 is quite similar, experiment.

I've recently 'been paddling a V12, which I believe has similar instability as a 560 (have only sat in a 560 for half an hour). The key for me is to find stability in myself and the paddle and not the boat. I.e. sit well upright and use your body and the paddle to stay upright and don't try to lean into the boat hoping it will hold you (it won't...). Let the boat kind'a do whatever it wants under you. Time in the bucket also helps a lot!

Going upwind in an elite boat is a core workout no matter how you cut it. Buddies that have 'been paddling 10x longer than me still curse about it, they just miss many fewer strokes than I do...

NB: if you have a chance to try a V10g3 do it, you might be surprised... (Swordie too). Could be an expensive demo...

shorten the paddle and increase cadence maybe?? Shorter paddles are less cumbersome when you are having lateral instability issues. Increasing cadence gives more flexibility in adjusting catch bracing. Timing of the catch in respect to wave peaks as suggested probably needs more focus..ry planting it just behind the peak maybe

To do "a little brace every 5 strokes" certainly does not do you good.
Try to work on your stroke as said in other posts, and then convince yourself that you can paddle upwind without bracing, relying on your forward stroke for stability. Try to find flow even when going upwind, maybe cut the waves at an angle to get softer over the top, relax in the boat not to loose your technique.
It's not so much about technique (you can go downwind, can't you), it's about confidence.

I was finally able to put all of your advice into practice and it worked really well. especially paying attention to the rhythm of the was helped a lot. I managed to get the paddle in just after the crests most of the time and was able to keep the boat moving. Thank you all for your advice.

I've been pondering on why we feel so much less stable upwind than downwind. If you're travelling against direction of predominant waves there are many more interactions between your boat and the waves so disruptive forces coming much more frequently and potential to get wobbly while on peak of wave occurring much more often. When going downwind you and the waves are travelling together so the interactions are less frequent and occur more gradually.
The most stable position seems the be when surfing and when perpendicular to face of wave. When the nose of the ski is right out of the water I imagine that my body weight is then able to press the middle of the ski a little further down in the water creating a wider base (via higher waterline).
I hope my pondering makes sense without just stating the obvious.

I believe that the dynamic stability also plays a role. When your surfski is stationary it is the least stable and as far as I can tell the higher the speed (within reason) the more stability there is. Since you typically go faster downwind you have more stability.

I also found that keeping the nose of the ski down helped a lot. trying to lean so that the ski stays in contact with the water as much as possible  meant that the ski didn't get blown over by the wind as much and helped keep the boat speed up.