With my self cleaning oven, I was told to first wipe out any heavy deposits before starting the cycle. Otherwise the heat from the self cleaning cycle will burn up the deposits which you will need to wipe out if they were heavy.
Sounds like you don't want to use the self cleaning cycle. I don't understand. I know of no other way to clean a self cleaning oven, tho I suppose you can use a product and ruin the self-cleaning feature.
Wait a minute. Do you have a continuous clean oven rather than a self cleaning oven? I think I've heard of ovens that continuously clean and do not have a cleaning cycle. If that's the case, I suggest that you have to wipe out excess food after each use. Again, I've not heard of a way to clean it.
If it's continuous clean without a cycle, I might try heating the oven u[ with a bowl of vinegar and water. The condensation from that my loosen anything stuck on.