I believe it is. Picture 004.pdf shows a view looking down on the valve, filter, and tank. In my version (which is probably higher resolution than what I was able to post) there's an arrow visible on the filter (not the green one I added). It shows flow entering via the flex hose and then exiting right into the tank.
Assuming your direction of flow throughout the pump and lines is correct then this would make sense.
Sorry the photos aren't great. The pump sits right behind the front grill, below the battery. I've removed the hood and battery stand to get to the pump. The photo showing the pump (006.pdf) is looking straight at the tractor. I'm standing in the FEL bucket. The lights would be about a foot above the pump and shining right into your eyes. I agree that the suction line makes an akward 180* turn just before entering the pump. I thought cavitation might be an issue, though I hope it's air suction.
Cavitation is essentially air turbulence caused by scarcity of fluid to be pumped through the system. That's why I question the possible uphill run of the supply from the tank to the pump, AND it's shared and narrow bend 180* turn, with the current fittings... This could be a flow restriction point that allows the pump to get ahead of the fluid flow? Hypothesising here...
If I were to remove the valve from the system and plumb the tank to the pump then to the filter and then the tank that might tell me if the valve is too limiting? I have run this pump once before when testing to see if it worked. The fluid was milky and garbage, but I don't remember the fluid getting frothy.
Can you describe further how you ran it? Was the direction of flow the same as it is now?
Do you know the rotational direction of the tractor's front shaft? Clockwise or CCW?
Is it possible the noise you hear when using the FEL valve above idle is the pump straining- bad bearing, cavitation, etc?
Is there any problem with pumping straight through the filter?
Only if the filter's particle size is too small and therefore restricts the flow/return to tank.
I used a teflon paste on all new connections. I suppose a tight but not sealed fitting is possible. Would suction show up using soapy water?
I think so, but not sure. I think if there is enough suction, the soapy fluid would be drawn into the site of the leak.
Neither and I

I do appreciate all the suggestions. I couldn't get away from other things to work on this today but did have internet access so I've been doing more research than fixing. Hopefully tomorrow. Besides, it's supposed to be warmer tomorrow (high of 19F instead of today's 10F).