For me, the down side would be that the knives are not located where I do any cutting, and it would be a pain to reach around/over hot pots and pans to get to the knife I want.

Agreed. My slide-in range came with a stainless steel piece to put between the back of the range and the wall. I'm surprised you didn't get something like that with yours. You might look to see if it's something your range manufacturer makes. Some people have a strip of their counter top put behind their range. I think that looks nice for continuity. Is that something you can still have done?

Depends on the range but with mine, those knives would get very hot. Even if I only used them cold, I'd expect any plastic or glued bits to degrade rapidly. Where does your oven vent?

Good points! I was focused more on aesthetics. Hadn't thought about the heat or simply the fact it isn't in my prep zone. Then again, even if I used a knife block on top of the counter or in a drawer, it would technically be out of the zone. Hmm....

I'll look into the trim for the oven. Another option I hadn't considered! @funkycamper, past the point of using the countertop material. That would have looked nice.

Our counter goes behind our slide in range too. I thought about putting a knife slot like those near my prep area, but opted for a knife insert for our drawer from ikea.

How about a removable granite or counter material piece, with w wood support underneath (not removable every day, but down the road if you get a different range)

http://www.housetweaking.com/wp-content/uploads/2012/06/appliance-review-10.jpg

Or this: http://www.microtrim.com/slide-in-range-filler.htm

Since your range is gas I would not even consider this.

Grease! The knives would always be dirty.

What about some sort of stainless insert, where you can stand drippy lids and utensils?

Thank you for the suggestions and thoughts! Again, more I hadn't considered. We played around with the oven, and it vents in the back. Best just go with the trim piece Frigidaire offers. Now to decide- black to match the top of the oven or white to match the countertop.

An idea for the knives- Love my under cabinet knife storage. You can't see it from eye level and the corbels hide it from view when we are sitting at the table. Mine is the Ikea one. It is SO handy. I have the rest of my knives in a drawer but reach for one of those perhaps only once a month.