When my grill grate gets too gross, I just buy a new grate. There are universal fit ones for 20 bucks around in Walmart/target/Tru Value/Lowes, etc....Depending on where you live they would be in the stores year round. In snowy areas, they will come out when the spring stuff begins to emerge.
If you want an exact match your grill brand, you can get them just by googling your brand grill + grill grate and find the best price.
I find the universal fit ones work just fine.
Way easier than trying to make a gross grill clean again. For ME, I would rather just get a new one. Call me lazy 
If you do want to clean,. I agree with the ammonia in a trash bag. Lay it flat for 24 hours and it cleans up OK. A bit messy because all the gunk turns to sludge and you wipe it down. Also need to do this outside because of the fumes.
I would not use your self clean oven. It will wreck the grate.