I am suspicious of dish racks on most counters except solid surface. Trapping water between plastic and engineered stone can be catastrophic. Careful, please.

You need landing/work space on both sides of a sink. Post your new plan and maybe we can help you solve the problem.

I have no idea why you would have clean dishes in the rack while doing prep. Do you not have a DW? Maybe provide more info or pictures . I have never used the drain board to hold hold a cutting board so I am confused.

If I understand what you are looking for.........how about putting a cutting board in a jelly roll pan on the counter to prepare meats, etc. Wash & put away to allow use of counter space for other things after the prep. No need for cleaning caddy to be on top of the counter, put supplies under the sink or on a shelf attached to inside of the door under the sink. If you have a dishwasher, use it and enjoy the freedom of not needing a dish rack.