I see, you're asking if the sloped walls will be a problem because the replacement mattress is thicker thereby effectively reducing the clearance. I would say you wouldn't have a problem with the headboard. Unless you sleep with your head up tight against the headboard in order to get your feet on the mattress that is. In that case you might be able to slide the mattress down 3 inches and fill the gap at the head with a couple of one dollar pool noodles.
For the sides you could obviously ignore the gap and see if as a bonus that makes it easier to make the bed. Or slide the mattress to one side or the other and see if you can fill the gap with a 1x6 pine shelf board sitting on some 2x4 or 4x4 pieces as spacers.
Other than that you might find the bed platform a bit heavier to lift with the thicker mattress. To fix, you can unscrew one end of the supports and remount them slightly more vertical so they can hold some more weight.