The only way to get rid of the "air bubble" is to use only opaque filters so you are not aware of the bubble inside every inline filter.
I groan a little every time someone brings up the subject.
It actually is not air inside there anyhow.....it is gasoline vapor that naturally forms in the head space above the liquid. You could purge or bleed off all the vapors and in no time at all.........the vapor head would be right back again.

You need to check that the vent hole in the fuel tank cap is not clogged, preventing the tank from breathing in air to replace the consumed fuel.

If you have made a direct correlation between descending grades and the rough operation of the engine, it may be due to the carb float not adjusted to specification.

I just experienced the same filler tube problem on my John Deere L110. It seems like the filler tube fitting must have vibrated loose over the years. In my case it was not completely off but the tube had crimped against the bottom of the tank. When I tried to move the tube to relieve the kink the fitting inside the tank came off. It seems like the fitting could be threaded back on and the tube replaced with a flexible one.

The concern about the pickup tube being loose as it goes into the tank would be letting debris in. Clean the area, a touch of lube and re-install the bushing , lube the tube assy and put it back in. If the tube assy is cracked- replace it. More than likely if the runability changes on grades- its normally water or debris in the bottom of the carb bowl. Unfortunately, no float adjustment to be made- but a float valve that is worn could emulate the same condition.

I was just having similar probs with my L110 with rough idling and eventually it would just die as soon as I started it up. This problem is actually even more similar to the '09 postings where the throttle was moving back and forth on its own. I Changed the gas filter, cleared the lines, changed spark plug, checked that the gas line inside tank was still attached...
I'm no pro mechnic, only a DIY'er, but HERE'S WHAT WORKED: underneath the carb bowl is something I'll refer to as the "gadget" - some kind of sensor with a red wire attached. It's part of the bolt assembly that secures the carb bowl. You have to decouple the red wire in order to unscrew that gadget and remove the bowl. With the bowl removed, I noticed two small parts sitting loose in the bottom of the carb bowl - a small, white nylon washer and a small, black rubber "cap" for lack of a better word. They looked like they originally were most likely fitted to the top of the "gadget", and they were. (If you don't see them or lost them trying to drain the carb bowl earlier, you need to replace them.) To reasseble, put the threaded top of the gadget back into the carb bowl hole, place the nylon washer over the top of gadget and the black rubber cap on the top of the gadget's pin-like head, carefully thread the gadget back in so you don't knock those pieces off. (Remember, the gadget is the "bolt" that holds the bowl in place; maybe somebody will tell me what that gadget is someday). I had the air filter off already, so after I started the engine back up, and it stayed running (!), I sprayed some carb cleaner into the carb thru the air intake. Oddly enough, spraying the cleaner makes the engine stutter like it did before I fixed it.

Your gadget is the "anti-afterfire solenoid". Its function is to stop the flow of fuel into the MAIN jet of the carb the moment you turn off the key switch (when you are stopping the engine).
Lest any reader get the impression that the small washers were not in their correct positions (prior to your removing the bowl) and that placing them into their rightful positions corrected the problem...............no.
If the washers had not been in the correct places already, the defective condition would have been "fuel leaking from carb bowl".
I would venture to guess that in your/this case, the "rough idle" was caused by water having segregated out of the fuel (stratification) and formed a layer or glob of water on the bottom of the bowl. This layer of water may "stir up" when the engine is started. The small droplets of water that arise from the stirring of the bigger blob can be drawn into the very small passages that comprise the IDLE or PILOT jet of the carb, effectively blocking fuel flow through them or at least causing the fuel to flow erratically.
Small water droplets typically has little or no effect on fuel deliver through the larger MAIN jet.
Water in the fuel supply (before you put the fuel in the tank) can cause fuel starvation issues if enough water collects in the gas filter that it forms a film of water to coat the filter media, obstructing the flow of fuel through the media.
Water formation or segregation in fuel system components will continue to be a scourge due to ethanol blended into today's gasoline.
Ethanol just "loves water" and will absorb water vapor right out of the atmosphere. This begins to take place inside the underground storage tanks at your local gas station and continues even after you pour it into your OPE fuel tank.

After cleaning my air filter, I can't get it to seat properly for re-installing. When I screw the cover down, it has a wobble rather than being secure. This hasn't happened before. Any suggestions?

I was having fuel issues with my la 110 and I by-passed the fuel pump with temporary fuel gravity fed to the carb and it ran fine, so I replaced the fuel pump. It has ran fine for about six months, but now it died while idling as dumped the grass catchers and I can't get it started. I tried the gravity fed fuel supply again, but it will not start. I checked the fuel line out of the filter and was getting fuel. Now I don't know where to go from here, any ideas?