putting the strap over the seat and pulling it tight on both ends on the deck will not work.
Picture doing that with a rope, and in place of the seat there is a pulley, as you lean the bike from left to right the rope goes over the pulley, and the bike is fully free to fall over either way.
Ok.. replace the pulley with your seat - now all you have is the surface friction of the strap touching the seat - not a lot of force there, no matter how hard you pull the strap tight.
You need a strap on the left side in a solid connection with the frame somewhere to keep the bike from moving at all to the right, and another strap on the right side to the deck. Both must be connected to the bike, not looped over it, and not wrapped around anything.
I learned this the hard way going on a camping trip with a sea-bag on my passenger seat. I had bungee cords and ropes going over the bag from one side to the other (like your proposed straps going over the seat), but there was nothing stopping the bag from rolling right and left under the straps.
I had to stop twice with in 10 miles from home, the bag kept rolling to one side or the other - I kept pulling the straps tighter, to no avail. I had to take all the straps and ropes off and start over, using the handle in the middle of the bag as an anchor point.
strapping stuff solidly to a motorcycle and strapping down a motorcycle is easy, but there are wrong ways to do it that look like they are secure, until the suspension compresses a tiny bit on a bounce, and the bike falls over.