Place havarti and cream cheese in freezer for 15 minutes while marinade is prepared.

Whisk oil, red wine vinegar, white wine vinegar, sundried tomatoes, parsley, green onion, olives, garlic, sugar, oregano, lemon pepper, salt, and crushed red pepper together in a bowl until well combined; set aside.

Cut havarti block in half lengthwise, then cut each piece into 1/4-inch slices, to form squares. Repeat with cream cheese.

Alternate cheese squares in a shallow baking dish with slices standing on each edge and sandwiched against each other. Pour marinade over cheese, cover, and refrigerate for at least 4 hours, or up to overnight.