What are some ways to connect my mining pool to another mining pool without altering any settings on the miners?
Outsourcing to a larger pool is definitely possible and can help reduce variance. Conceptually, to them you're just a very large miner. On your side, instead of submitting a found block directly to the network, you submit it to the larger pool, and any shares you accept can be passed on the larger pool. (Regarding difficulty settings: Having different difficulty settings between your miners and the larger pool is find as long as the larger pool's difficulty does not exceed that of any of your miners. If that is the case, you must either bring down the difficulty of your miners or convince the larger pool operator to raise your difficulty (which they may very well agree to, since it reduces the load on their stratum).
For the actual implementation, I'd talk to someone who's done it before. TradeMyBit outsources its LTC and DOGE mining to MultiPool. I've talked to the owner merc before, and he seems like a nice guy. You could try contacting him here to see if he's willing to give you any tips.