So, you'll want to walk just over 300 km, if you stick to 20 miles a day. Leon is 311 km from Santiago, so if you walk as fast as you are planning, you will have no problem making it to Santiago in 10 days. However, that isn't allowing any time for injury or other unexpected things that might delay you. If you are really fit and used to walking with a pack, that is what I would recommend!
The only thing you want to be careful of is that in the last 100 km, the trail can get very very very crowded. If you don't finish walking by noon, all of the beds can be taken, so you won't have time to walk 20 miles a day unless you reserve a bed ahead of time in a private albergue. It shouldn't be as busy in the beginning of April, if that is when you go, but it is something to keep in mind.
If you want to start closer, you could maybe start in Astorga, which is 260km from Santiago. The next closest town of any size that you could probably get to is Ponferrada, which is still pretty small, and it is 203 km from santiago.
Buen Camino!