How do you keep your core muscles in shape?
Excercises alone aren't enough to tone the core! Food intake is very important to consider when aiming to strengthen your core!
Really?  What types of food items are important to toning the core?  
Portion control is very important. No over indulging or an excessive amounts of calories should be taken in, if you're looking to tone up quick
Are there certain foods from which I should steer clear?
The food pyramid is very helpful when deciding to choose what foods to eat in order to maintain a well balanced diet
In your professional opinion, would you believe that a low carb, high protein diet would be best?
I think that's a good choice! That diet is often recommended to build muscle but burn the pesky fat!
Wonderful!  Thank you.  Now, are there variations of the crunching exercise that might focus on toning the core?
Incremental weight increases in relation with crunches would definitely do the trick
With weight increase, are you meaning a weight laid across the chest during the crunch exercise?  
Pushing, bending and twisting with weight increases will have you ready for summer!
This is a great help.  Thank you so much.