No offense Smokey Wren, but you are comparing apples to oranges.
If you are towing your trailer with the vehicles in your signature, I can see why you definitely need a WDH. You are about equal on trailer weight versus tow vehicle weight. That is a recipe for disaster without weight distribution.
The OP is proposing to tow a tandem axle trailer (at about 4000 lbs) with a 35-foot motorhome that weighs about 20,000 pounds. All that with 228 inches of wheel base. He has a 22,000 pound chassis with a Gross Combined rating of 26,000. He is going to be close on weights, but I'm not so sure on the WDH.
Here is the rub:
His MH is rated to tow 5,000 pounds with 500 pounds of vertical tongue weight.
That's it. At least that's all Winnebago says it has.
Winnebago should give you the definitive answer on whether you can use a Weight Distribution Hitch or not. When the manufacturer says 500 pounds of vertical only, this usually means no weight distribution allowed. You get 5,000 to play with and that's with only 500 pounds of weight on the hitch.
When you tow 4,000, you should have about 500 pounds on the tongue. You will have to load that dead on even to avoid being tongue light which could lead to sway. You may be able to use some form of sway control without WDH if Winnie says, "NO" on the WDH. Those type of anti-sway devices are primitive and old school, but may be your only option for sway control. That may be your biggest problem if you can't get enough weight on the tongue to keep it stable.
The OP asked about clearance, so I thought I'd add a suggestion to help him with his perceived clearance problem. Maybe he has already eliminated the WDH and that's why he didn't ask about it?
Maybe Smokey and i got off on this tangent and it helps. I hope so. We buy these huge buggers and think we can tow a whale. When in reality, the weight ratings really stink when you look at them.
If he loads the trailer properly and has to use a drop bar to keep it level, he should be fine. The drop bar will get him 5 or 6 inches more clearance.
I would recommend a short trip with a little testing. In reality, as soon as he drops the tongue on the ball, he should have an idea. If you get some squat, the trailer may be too much additional weight. Your MH may have to stay on a permanent diet to tow that trailer.
Here's the rub. Do the numbers on your motorhome. Manufacturers have played fast and loose with the chassis. They will build a 19,000 pound MH on a 22K chassis. After add ons, you got nothing left for cargo carrying capacity. So, if you load your motorhome up and drop the trailer on the hitch, guess what? All of a sudden your front end is up and your back end is squatting. You are over loaded.
Go to a scale and weigh the MH ready to travel. That is cheap insurance before you buy a trailer too big.
They do make WDH hitches that are adaptable to those short V-nose trailers. Some of them aren't for the faint at heart. Some require drilling into the trailer frame. That's something I'd avoid at all costs. He may have a little room to work under the box. It looks like there is a little gap with access to the frame for a WDH. Maybe?
Whatever you do, find out from the real experts first. Call Winnebago.
If they give you the OK on a WDH, you will know that if that is needed, you can go that route. My guess is no. If a WDH is authorized, that OK usually comes with a higher weight rating and hitch weight rating. It would say 500 vertical and 5,000 tow AND 1,000 tongue weight with WDH and 10,000 tow with WDH. That's why I have my doubts.
Good luck in how you go.
By the way, I tow my Jeep 4 down with about the same numbers that you have. It weighs 4,300. Pulls like a dream with power to spare. I do not have the tongue weight problem you are going to have. Tow bars weigh very little.