BF90D - Oil Consumption + Fuel Consumption + Black oily residue on back of leg

Have a BF90D, Used in salt water since new (I am not the original owner). I have a black oily residue on the back of the leg below the exhaust port. In about two hours of steaming at 5000RPM I burned almost a quart of oil ( I use the Honda recommended oil). In those two hours I burned over 10 Gallons of fuel.
My inlaw has some hull with a 70 Yamaha and burns about 5 gallons for same distance also running at 5000RPM.

I have replaced both thermostats, oil change, oil filter, High and low pressure fuel filter. I figured the thermostats were the issue as the engine would think it was cold so adding too much fuel (choke) which would explain the fuel consumption.
No smell of gas in the oil but the oil feels like it is diluted, it smells like exhaust this was after a total of 3 hours running.

Any ideas?

I wouldn't run that engine if it is using that much oil. Only a couple of ways to burn oil like that. Worn piston rings or issue with your valves. A compression test would confirm that issue. Pray it is a valve issue which is still a spendy fix if you are not handy with a wrench. Maybe run some decarb through it from a separate tank to see if that might break up carbon build up on the valves. I am sure there are other types of fuel additives that might help fix the issues without tearing the head off.

First thing I would check is fuel pressure and get someone to do a running data check with drH to check sensor values. It sounds like this engine may need a rebuild, valves will not cause this amount of oil consumption , how many hours has it done and what do the spark plugs look like, they would tell you a lot about what's going on inside the engine?

I agree with the above advice.....don't run it anymore until you get this sorted out and looking at the plugs might reveal what's happening. Especially if it's one cylinder in particular that's causing the trouble.

If looking at the plugs doesn't single out one cylinder performing significantly different than the others, some testing, as in compression, may be in order.

However, if this were a car and I couldn't see anything obvious with the plugs, I would first want to inspect the PCV valve for being stuck open. This would allow uncontrolled crankcase vapor, which can be laden with oil droplets, to enter the intake. If the vapors carry significant oil to the intake then combustion will be adversely affected and cause the poor fuel consumption and exhaust "drooling" you've noted.

I looked on boats.net Honda parts but couldn't readily find a PCV for this outboard. I don't work on these so I don't know the strategy for venting the crankcase or if Honda has another name for PCV (positive crankcase ventilation)

Hopefully someone else here might have that information for you.

Good luck

Honda outboards don't use PCV valves, they breath through a baffled labyrinth in the tappet cover from the air intake silencer.

Ok then...there you have the strategy for relieving crankcase pressure. You may want to look to see if excessively oily residue is entering the throttle body through the silencer.
It wouldn't be that unusual for that baffle to come apart. I've read about newer cars with plastic valve covers having the baffles come unglued although I haven't seen it myself.

Good luck.