You can place a layer of cardboard over the grass, and then top it with soil. Enough to keep out the undesirable grass, and it will break down over time. Try to avoid cardboard with colorful dyes and keep to the basic brown.
Solarizing is the easiest way to do this, but it takes a lot of patience. Depending on your area you may need to start now to have your site ready for spring planting. Search for a guide on exactly how to do it, but basically you cover the grass in clear plastic to create a greenhouse effect that will kill the grass and any seeds. You water before putting down the plastic to encourage seeds to germinate. Once you're done (four weeks minimum, more is better) you remove the plastic and plant your plants.
Depending on the type of grass you have, tilling may not be effective. It also may be very difficult if your area is as rocky as you say it is.
Another option is to use a shovel to dig up strips of sod and flip them over. This should be almost as effective as solarizing, but it's much faster (no waiting) and much harder work.
If you have the time to do it, it's absolutely the best and easiest way. It's hard to postpone landscape projects, but doing them in the right season is setting up your project for success. Good luck, and don't forget to take progress pictures!
I replaced a grass yard with clover a few years ago and didn't have much success with any of the "cover it until it dies" methods.
Chopping the sod wasn't good for me either, so I gave in and used Agricel Grass Out a clethodim herbicide that only targets grasses.
According to what I could find, it isn't harmful to birds or bees once it dries. It dissipates in the soil in 3 days. It is slightly bad for fish but that's only a concern if you spray directly next to a stream/creek.
I cleared an area of lawn for my container garden years ago using a tarp. I just covered the area, using lawn staples to keep it down. The next year, the grass underneath was completely broken down, barely any remnants being left.