Actually, you can remove the engine access panels by folding the left seat support leg, unlatching the panel, and tipping it as you slide it to the port side and forward. But it is still not that easy.
I assume that you get about half a bowl of water because the hand pump is not sealing and the water level in the bowl is the same level as the lake. If you have water on the floor then that could be a problem. I had the hose connecting the top of the pump to the top back side of the toilet leak twice. Once was a hole and once was a loose connection. There were not any clamps on this hose on mine. Look things over. Dry up everything. And start looking and feeling for leaks. Check all hoses from end to end A dry paper towel will show water sometimes.es when your hand may not. I know, nobody wants to be the "head mechanic".
You may need to try a rebuild kit or another hand pump. Hope this helps.