I'm using someone else's picture here since I can't make my own at the moment. I think you're best bet will be to build a small "platform" out of the 2x3's and then set that on top of your saw horses:
The platform only needs to be big enough to comfortably hold one full plank of flooring, so the total size of 40cm x 150cm should be good. Draw it out and make it a little larger if you have enough 2x3 lumber (or smaller if you don't have enough). The cross pieces of the platform will provide more support to the planks and provide additional clamping area.
You will have to cut into the platform when making rip cuts, but just adjust the blade to barely cut through the planks (you're doing that already, right?) and it won't be a big deal.
For cross cuts, hang the edge to be cut off the side and clamp the long end securely to the platform. For repeated cuts, you can even put pencil marks on the platform to line everything up quickly.
I just noticed that you have 6" clamps - you can modify the design of the platform as needed. You may want to lay the boards down and attach to each other like a train track (with the cross pieces on top) for easier assembly and a narrower clamping surface.