Hello Kriskros. I'm duplicating the pm's we have exchanged with this forum post, so as to complete the loop with everyone who has tried to contribute.
For some reason, I cannot locate pictures of your completed bike. If you'd like, you can send some to me to help me visualize your bike.
Have you tried pedaling "in a circle"? That technique might help. Perhaps you already know of it, but if not, I'll try to explain.
Most casual bike riders only press down on the pedals. So only one leg at a time is doing any work. Avid recreational cyclists and professional cyclists wear special shoes which attach to the pedals with cleats. Because the shoes are attached to the pedals, the cyclist can now not just push down with one leg but can simultaneously pull up with the other. To make that smooth and more powerful, the cyclist learns to apply some force to the pedal throughout the entire circular stroke.
Kriskros, if you are able to use cleats, then the above technique may work well for you. Without cleats, there is another technique. It is tricky, but if you can keep the shoe of the leg that just made the downstroke in contact with the pedal long enough to push it past its farthest travel and start bringing it around, then the pedal that is closest to you will have made it past its zenith and will accept a downstroke. The technique does require you to point your foot at the farthest point of the downstroke and then push the pedal not away from you, but down towards the ground instead. That brings the other pedal up and around.
If neither of the above works for you, then I suspect that you may have designed and built yourself a bike that cannot be pedaled due to the location of the crankset with respect to the bicycle seat. That would be more than frustrating.
Kriskros, as you then indicated, this was the issue and you may very well try pedal straps. Bon chance!