LoL... I guess we all deserved that!
On mine, we remove the cook-top grate, push the drip-pan forward and lift from the rear. The whole top is on hinges to allow you access underneath the drip-pan. This will allow you to get all the crumbs that fell underneath the burners.
The quality of the finish on the stoves seems poor in comparison to a regular kitchen stove; we don't use anything beyond warm soapy water or, in a pinch, windex (as you've suggested).
My previous trailer, we had to unscrew the whole top end of the stove and pull the whole thing apart to get at the junk the fell under the burners. Near the end I found a shop-vac did a pretty good job so long as the stove wasn't caked in crud.
DW and I share the cooking as we both get enjoyment out of it - the stove gets a daily wipe down after every use (same with the BBQ). The trailer gets continuous cleaning as we use it; every third trip or so, it gets a thorough cleaning top-to-bottom, unless we're doing longer-term camping, whereas it gets a solid tidy as necessary and a full-service cleaning whenever convenient.
Do I get a C- for at least trying hard?
3 kids and Buddy the Dog;)
2010 JayFeather 23K
05 GMC Envoy XL