I think your link is a good start; whole foods is the way to go. A lot of people SEEM to benefit from a Selective Carb Diet (I never followed this rather strict protocol as I already found a personalized protocol to keep MY symptoms at bay, but if I started having problems I would consider it. See my post by searching: MY Supps for MY Dis-ease) I'm not familiar with "constipated crohn's", but here is my opinion post I made as my advice to someone who is currently having problems:
Personally, I could handle white flour/processed grains, but for only so long. I think these foods have a longer, slow burn effect, so to speak, and ultimately kill off good bacteria. Sure, the effects aren't as immediate--for me--as sugars (HFCS,aspartame,acesulfame potassium,sorbitol,sugars,crystalline fructose,...just use stevia or honey sparingly) or caffeine.
After determining whether you're sensitive to lactose or gluten, or not, I would stick to a modified low residue diet: chicken, hard boiled eggs, sweet potatoes, butternut squash, herbal teas (ginger, peppermint), cooked carrots, steamed broccoli, vegetable drinks (100% juice), bananas, other 100% juices. If your not sensitive to lactose, I'd take an unflavored whey protein with a banana, cinnamon, handful of nuts, and stevia/honey in a blender with cold water.
Maybe search the site for safe foods. Personally, I would maybe cut out grains for now and slowly introduce sprouted bread (like Ezekial's orange bagged, frozen bread). Maybe make smoothies with nuts or nutbutters and sweeten with stevia or REAL raw honey (upwards of 70% of store bought honey is fake).
If I were flaring, I would eat one food at a time and not combine fruit or its juices with other food groups. I would also take enteric coated fish oil (3-4 grams of Omega 3, a day) and good probiotics (Jarrow EPS is cheapest on iherb.com) at least 15billion (depends on brand though) a day. Additionally, S. Boulardii is specifically helpful for diarrhea (I'm currently taking a NOW product of this).