The 8 hours a day is what makes your situation challenging, more than the 7kH/s. Controversial as it may sound, I would consider mining on the largest pool I could find, the one that finds the most blocks per day, giving your 8 hours a better chance at getting paid. I haven't checked the numbers mind you, so DYOR.
Monero Mining
DO NOT CONSIDER MINING ON THE LARGEST POOL.
seriously, there is no benefit to it. on p2pool you can be paid out every few hours, using ANY centralized pool you will have to wait for payout thresholds and then pay transaction fees (and potential pool fees) on payout. in addition, centralized pools can steal your funds.
if you dont know how to use p2pool, check out the gupax guide its even easier than setting up with a centralized pool (linked in the sidebar).
You do realize, part-time mining you could be shooting blanks for days mining on a smaller pool (p2pool included). Keep that "ANY centralized pool"crap out of here.
10 shares weighed at 10 is the same as 1 share weighed at 100. If you mine centralized, youll get a bunch of low weight shares and wait days or weeks for a payout and lose say 5% of it to fees. If you mine p2pool youll get a high weight share every day or so and get paid out immediately.
"shooting blanks" means nothing when your hits are way way bigger.