The only other option is to Attach a Mounting Strip:
If your quartz counter does not have a plywood support and your dishwasher has some room between its top and the counter, consider installing a wood strip to the counter for the dishwasher to attach to. Cut a strip of hardwood, such as a one-by-two, to the length of the dishwasher opening. Use a silicone adhesive to attach the strip to the quartz just above the mounting clips. Adjust the feet on the dishwasher to get the mounting clips level with the strip and screw the dishwasher right into the wood. Take care not to screw too far and crack the quartz.
If you'd rather purchase a new Kenmore dishwasher that is compatible with side mounting clips, all new Kenmore dishwashers with a prefix of 665 are compatible with side mounting clips. These are the mounting clips that will work with new Kenmore dishwashers with a 665 prefix: searspartsdirect.com/product/5ayxwmfkzi-0022-665/id-8212560
As an example, let's check this dishwasher: sears.com/kenmore-elite-24inch-built-in-dishwasher-stainless-steel/p-02214743000P
To check to see if a model is compatible, being typing the model number 665.14743 (don't hit enter yet) under "WILL THIS PART FIT MY MODEL?" You'll see that it fits once you select any one of the ones that show up in the list. For help with parts, call Sears PartsDirect at 1-800-366-PART. To find the prefix of the dishwasher, click on Read Full Description on the product page, and click on the owners manual.
All Kenmore dishwashers: sears.com/appliances-dishwashers-built-in-dishwashers/b-1020283?Brand=Kenmore&Brand=Kenmore%20Elite&filterList=Brand&searsTab=true