You are not alone is this basement air cooling problem. I understand that Winnebago has upgraded the basement air capacity for their 2008 year models. We like our indoor temps much cooler than the basement air can handle, and we are in the same boat.
I have had similar problems with my basement air, and YES, you will have to remove the rear cap IF you have a seperation at the TOP of the "Y" where it splits off to both duct runs, or to check to SEE if you have a split duct up top. Typically, there have been some problems in the main duct right BEFORE it splits to two ducts, especially in the 2003,2004, 2005 year models. Winnebago has repaired most of these that I have seen like this.
This is the best way to check and see if you might have a hole or split in the duct running up under your rear cap:
Run your air conditioner for a bit, and reach up as high as you can with your hand and feel around the ductwork for any cold air seepage. Buy one of those temperature IR guns ($50 at Pep Boys..they're also great for checking tire temps or brake rotor temps!), and reach up under the cap and aim it toward several places in the duct work to see if there is major temperature difference.
Also keep the following information in mind. Your indoor air temperature differential should be 15-20 degrees cooler at the closest vent from your air intake. So, if your air return (where the filter is) is 70 degrees F, your closest ceiling vent output temperature should be 50-55 degrees F. This has NOTHING to do with indoor/outdoor temperature differentials, and if someone tells you that there should be a 15-20 degree differential between the outside and inside temps, they are ABSOLUTLY WRONG!
Also. I have talked MANY times to RVP (who makes our air conditioners), and they specifically told me to use the CHEAPEST fiberglass spun filter you can find for the inside air return, and if you should be able to "see your hand through the filter". Another words....this shouldn't be one of those pleated fancy ones. Change these out often.
The key is to get LOTS of air flow out of the vents. Keep your fan selection on HIGH MANUAL (on all the time) and when the condensor clicks off, the fan runs still.
Someone also told us once that you shouldnt be able to run your hand over the rear cap and feel cooler temps where the duct runs....this is not true. Once we were in San Antonio on a 65 degree morning after running the air all night (to keep it 65 degrees inside where we like it), and I noticed a heavy dew on the rear cap EXACTLY where the duct was and even where it made the split near the top to the two ceiling duct runs. This doesn't mean I had any leakage, but that the rear duct run isnt insulated that well.
Winnebago is known for their superior manufacturing process, but not known for their insulating ratings. I definately wish they would insulate these better. I have an old post on another forum where I used my IR Temp. Gun and measured the temperature where the roof is attached to the walls (inside the motorhome) and it is attached by an un-insulated long extruded aluminun section that runs the length of the motorhome and the temps were in the 90 degree range right there on the ceiling/walls area where they are attached. Run your hand up there sometime when the Sun is beating down on your unit.....it will almost burn your hand.
We have done a few things to help the cooling issues with this basement air. 1. We installed a window awning over our long side window. 2. We cover our windshield with Sunguard 94% UV covers. 3. Use vent pillows to stop the heat from entering the roof vents. 4. Start your air conditioning FIRST thing in the morning to not allow "heat sink" to set in.
Hope this helps.....as your complaint has been very common, and we have learned to live with ours, but not totally happy. :-\