Mission accomplished and very happy with the results.
We made the first batch from start to finish with the cheese added.
I added about two table spoons to the pasta and there was plenty enough zing that I didn't need any seafood sauce for the shrimp.
We found that only using scapes in the first batch was a little overpowering so we went 50/50 scape and dill for the remaining batches. There is no cheese in the jars and it will be added once it's thawed and we're ready to eat it.
Here is the recipe that we used. We went 50/50 scapes and dill and used grated parmesan cheese instead of the one recommended.
Ingredients
1/4 cup pine nuts
3/4 cup coarsely chopped garlic scapes (see note)
Juice and zest of 1/2 lemon
1/2 teaspoon salt
A few generous grinds of black pepper
1/2 cup extra virgin olive oil
1/4 cup grated Parmigiano Reggiano cheese
Directions
In a small, dry pan set over very low heat, lightly toast the pine nuts, stirring or tossing occasionally until just beginning to brown, about 2-3 minutes. Remove from the heat and let cool for a few minutes.
Combine the scapes, pine nuts, lemon juice and zest, salt, and pepper in the bowl of a food processor fitted with the blade attachment. Pulse about 20 times, until fairly well combined. Pour in the olive oil slowly through the feed tube while the motor is running. When the oil is incorporated, transfer the pesto to a bowl and stir in the grated cheese. If you plan to freeze the pesto, wait to add the cheese until after you've defrosted it.
Notes - You can use half scapes and half herbs such as basil, dill and chervil if you prefer.