Is there any kind of predictable lag between the time you start eating and the time blood sugar starts to rise? Is the rise in BG due to the actual digestion of the food (which I would expect takes a while) or in response to just eating?
Gosh, I wish there were an accurate way to predict this. But it depends on the individual AND the meal.
Generally, the higher FAT content, the longer the time to digest and thus the longer a spike will take.
Higher fiber content also has a similar effect, though not as much as high fat seems to.
High Protein content also will impact the time to digest, but again, not as much as high fat will.
Refined carbohydrates will react faster - things like sugar, white breads, etc. Potatoes, especially mashed or well-baked, will affect most of us quickly.
(In fact, it's been proven that just the saliva in your mouth will convert cooked potato into glucose... before you even swallow!)
Complex Carbohydrates will cause a slower spike
(due to the slower digestion/absorption and the higher fiber content) than refined carbohydrate - to the point that complex carbs eaten with high fat can take 3 to 4 hours before a spike happens.
Fruits can impact how quickly you spike - The lower glycemic the fruit, the better. Your best bets for minimizing spikes with fruit are Berries. But we're all different...
Keep those things in mind and with your own testing you'll come to be able to estimate pretty well when and how much your meals will spike you...
Also, I often go to bed 4+ hours after a meal with a BG of 110, then sleep for 7 hours. When I get up, my BG is sometimes much higher (140). Since I had no further carbs, what causes this?
It's called 'Dawn Phenomenon' but to many of us it also happens during the day.
Some people simply refer to it as a "Liver Dump" - basically whenever our body decides our blood glucose is low, the liver will release more into our systems. One very common time for this to happen is just before we wake, for many reasons.
First, we are fasting typically for 7hrs or more, which is longer than we do during the day... if our BG's drop to what our body considers an unacceptable level, it will release glucose to compenesate.
Second, as we prepare to wake for the day our bodies go into a 'wake up' mode, releasing hormones which will also impact our blood glucose as it prepares us for our day.
For me, with my metabolism I can burn through my circulating blood glucose in way under three hours, so my liver is constantly dumping - especially during exercise where I burn from a 7.0 (126) to under 4.0 (72) in about 7 minutes. Luckily as my BG's have stabilized my liver only dumps what it needs, and typically my liver dumps result in less than a 7.0 (126) reading now.
I know the numbers are high, I was just DX'd Type 2 a few weeks ago and my doc wants to see how much impact I can have by changing my diet. I've dropped to about 60mg carbs/day and while it helped my Tri-G drop 60 points

my BG still seems to be all over the place for no reason.
I'm used to balancing stress (I'm bipolar) where less stress=less mood swings. I'm getting the feeliing that with diabetes less carbs does NOT equal lower BG all the time. It's a lot more complicated, isn't it.
Your doctor is right in suggesting diet changes - the lower-carb you can eat, the better for your diabetes control. Find what works for you, stick to it.
You'll likely find the stress complicates your BG's - that's something that's going to come with life with a BPD diagnosis - so be prepared for it and NEVER, EVER give yourself grief for when those elevated levels happen.
I had a cold/bronchitis that lasted over 2 weeks, and elevated my BG's about 20% as a result... Sometimes you simply cannot control it, but you do the best you can.