Type 1, (mostly) vegetarian, and fairly fussy eater as well. I was eating more typical fare up until about a year ago, but this led to an increase in my A1C (I was in 8 range) so I resumed as more low-carbish approach (under 140g.
I do eat fish; I had to add that to my diet because I needed the protein. At first, it was hard because, like you, I have texture issues. It eventually became a mind-over-matter game for me and I was slowly able to increase my food repertoire.
I stick to foods that are as minimally manufactured as possible. Lots of veggies and fruit (for me, fruit has never been a significant challenge to bolus for). I avoid bread, rice, and pasta as much as I possibly can. These are my "trouble foods."
I eat a lot of cheese and eggs. Strangely, my cholesterol is fine. You mention that your cholesterol is up but sometimes this goes up for reasons other than what you're eating. So you may be able to incorporate these into your diet without affecting your cholesterol.
I keep things like nuts, pistachios, and other whole, low carb snacks with me at all times. This is very important if you're busy and don't have time to always stop and have a full meal. I stock up at the beginning of each week.
I do eat quinoa and, for some reason, this does not have a huge impact on my BG (at least, not to the extent that I expected).
I have done a lot of experimenting with vegetable recipes that I find online. This year, brussel sprouts have been my favorite! Epicurious.com is a great site for finding new vegetarian recipes. I try to find at least one new recipe each month from there, either for a main or side dish.
A lot of the changes I've made in the last year have just been things that I have FORCED to become habits. I make sure to hit the grocery store each week and stock up on the foods that I know I can eat during the week without much fuss. I've found a number of frozen food items that are vegetarian, low carb, and easy to carry to work and heat up at lunch. This took some experimenting.
As for exercise - I do it as much as I can. I would say I'm very active, but even on days I can't be VERY active, I do whatever I can to aim for moderate activity. It may just be taking the stairs instead of the elevator, or going for a walk at lunch. Anything to get me moving will bring down my BGs and burn calories.