Small-batch all-grain brewing

I'm familiar with the fermentation process from my adventures with mead/wine, and I'd like to get into all-grain beer brewing. I'm planning to make a small batch (2 gallons) on my stovetop, and I don't have any pumps/coolers/etc. I've devised a sort of technique based on some posts/videos I've looked at. Will someone critique it and tell me if the results will be good/bad?

1. Heat mash water to correct temp.
2. Add grains and adjust heat to hold said temp.
3. Strain through fine-mesh colander into a second pot (wort pot).
4. Heat sparge water in original pot and add grains.
5. Strain a second time into wort pot and proceed with boil.

* I know there's a part where you're supposed to discard a small amount of wort until it runs clear; Can I just pour my finished wort through the grain bed one more time to catch these particles?

Filtering wort through the grain bed is a great way to clear it up, but not necessary. A lot of people here (including myself) have had success with the brew in a bag (BIAB) method, which is perfect for this kind of thing and only a slightly simplified version of what you posted.