My concern with your method isn't with using paper. If that works for you, outstanding. Go for it. All
carbon is good carbon.
But irradiating compost with a glass cover or putting it into an oven "until cooked" kills the best thing about compost: the microbial life therein.
As a soil amendment, compost has minimal N, K and P . . . there are nutrients in compost, but that's not why it's so beneficial to plant life. If you're composting a ton of
coffee grounds, for instance, yes, you'll have nitrogen rich compost. But for standard compost ingredients (garden waste, veggie and fruit scraps, grass clippings, etc.) there aren't high levels of N, K, P. But what there is is bacteria, fungi, and all sorts of microbial life. Compost feeds the soil food web by introducing a bunch of new microbes and the carbon that those microbes
feed on.
The reason why bare soil is so often infertile is that the sun irradiates soil life. In laymen's terms, the sun cooks the little critters and kills them. So hearing that someone might intentionally choose to cook compost seems to me to be counter-productive.
I'd much rather have a few rogue weed seeds popping up in my garden beds than spending all the time and effort to create compost, only to deliver a lifeless product to the garden after all that effort.
One other thought: weed seeds germinating in half-finished compost does several very good things. 1. It shows you that your compost is alive and a great medium to grow in. 2. Those weeds are pumping sugars into your soil (
root exudates). Let them grow for a bit before you pull them out, as any living root pumps life down into the soil profile and feeds the soil food web. Pull the weed before its ready to go to seed, but having a living root growing next to your garden plants is a good thing, not a bad thing. 3. If you let those weeds grow for a bit before pulling them out, its just extra bio-mass for the garden. Chop and drop, and let the dead weed contribute to the ongoing fertility of the soil.
I'd encourage you to read a bit more about soil food webs and what all those microbes are doing down there around the roots of your plants. This is where the magic happens.
http://www.soilfoodweb.com/
https://en.wikipedia.org/wiki/Soil_food_web
http://www.finegardening.com/introducing-soil-food-web