I do believe that protein contributes to blood sugar rise, I count half of the protein grams as carbs. Bernstein also recommends this. Also, morning is always a hard time for me. And once you low carb and your insulin levels drop, you can have situations where your liver dumps blood sugar (low insulin and rising glucagon starts gluconeogenesis). So something like exercise in the morning can be a real problem. It sets up the conditions for major Darn Phenomenon even if you start out low. Dr. Bernstein recommends against exercise in the morning for exactly this reason. I actually have to bolus for my weight training, otherwise my blood sugar rises.
Re your "trusting the pump" comments, what I learned from from the MM pump, even w/o the CGM is that if I ate really regularly which I do during the week as much because my job is nutso and I'm really just eating for fuel, the pump reports, splitting it up between at meal BG and post meal bg gives me a notion of the accuracy of my bolus settings w/ the post meal numbers and the basal settings w/ the pre-meal numbers. If they aren't coming out where I want them to be for like 3 days, I'll make adjustments until the BG is where I want it. It may oversimplify it a bit and, well, weekends can be crazy but it has gotten me to an ok spot and allowed me to pursue some of my other interests.
Second all the above advice. 50% bolus for protein has been working well for me. I've done away with dual / square wave. Apidra seems to peak in 1-2 hour lower my BG for 4.5 - 5 hrs. Seems to cover protein nicely if I take it all at once.
I don't always TAG, but if I'm eating a significant amount of protein and/or fat, I find it helps the later spikes (like your 4 hr pp one) a lot. For some reason if I have no carbs with a protein/fat, I spike more, and sooner. I've found combo boluses great for those meals, though it did take me quite a bit of trial and error to figure out what timing/% works for me.
If you eat that few carbs per day, you're going to need to keep track of the protein content of your foods, because your body will be converting proteins to carbohydrates. You're also going to need more insulin per carb.