I suggest Charlie's Soap all purpose cleaner. It is an excellent degreasser. I use it all over my home and have not had it damage anything so far.

We have a similar set-up with a painted hood encasement. I have used the Mr. Clean Magic Sponges with no damage to the paint and removing the grease coating.

I use Method all purpose cleaner on everything from the appliances to the cabinets to the baseboards to the walls (we have two Golden Retrievers that rub up on everything). It works really well at cutting through the grease on the stove hood, but has never damaged any of the painted surfaces that I've used it on.

If you can, I'd check with whomever painted the surround (it's not clear if this is a liner, part of the cabinet or the hood was painted to match the cabinet) in the event there're any warranty issues about cleaning agents. We have had painted cabinets and a SS VH for 5 years and have had no residue on the cabinets (including those that butt up against the hood and are directly along the side the range top--similar to yours). We have a grill and do major front burner stirfry and panbroiling. We've used fantastic and soapy water for general cleaning on the cabinets. VHs don't have filters, and you may want to check to make sure your hood's dampers are fully opening. There have been a few posts about dampers getting stuck (I know, I was one of them). However, if they were stuck you'd expect increased noise and diminished performance. You can check the dampers by removing the grease collection box as you do when you clean it (hopefully you've done this before)--the dampers will be small doors above the squirrel cage wheels and should open easily and extend to a full 90 degrees. The number of dampers depends on the number of blowers. You also should have a damper on the outside of your house wherever you hood cap is mounted. When the hood is on high, this should be fully open; hopefully you can check this from the ground. One question: do you follow the old restaurant rule of "stove on, hood on?" It took me a while to get the rest of the household to always exhaust, and to run the hood at a level high enough to clear the cooking area. If the hood is working properly on high and it's underpowered, I would think you could see smoke/steam rising outside the front lip and not being captured.

All: Thank you for the suggestions. I am now armed with some things to try.

Live Wire Oak and Teachmkt: I think the problem is that I don't use my hood as often as I should. I rarely turn it on - only when I have a bunch of steam from boiling pasta. I guess I need to start using it when I cook anything that has grease in it (or anytime I cook anything).

I appreciate all the input!
Try_Hard