I would suggest doing this:
1. Schedule both 10 man runs on the same night, get people to signup ahead of time so they are somewhat accountable to show up.
2. Split groups evening and pug the 1-2 slots that would fill out both groups.
3. Recruit more "casual" minded folks - grab pugs that are decently skilled, fill in class holes so you have 25ish folks competing for the 20 slots.
This also sets you up when both groups are finishing kara in an evening or doing all non-optional bosses in a single set to move kara to another night and start doing Gruul's lair since everyone is already playing at the same time.
That is how my guild did it. Many of our members play 2 nights a week. We started out doing just Kara 1-2 nights a week, made 2 Karas, then moved karas to off nights and did 1 night of 25 man. When ZA came out we transitioned to 1 kara and 1 za and 1 night of 25 man. Now we run 2 karas, 2 ZAs and 1 25 man. Still with most of us playing just 2 nights a week -- which is pretty casual - while setting it up fro folks that want to do more to fill in group gaps.
The beast is getting hungrier.