Wishing, you HAVE to hit 1200 calories. You're very tiny already and you need to be careful - trust me you don't want to lose your ovulation. I'm also only 5 feet tall, started the LE diet at around 107lbs and had to gain a tad because I started to see my ovulation go right off the rails.
Being so slim you need to aim to maintain - please don't lose any weight. It is still LE diet if you maintain but keep blood sugars low. And yes, your previous grazing is definitely boy friendly, but otoh if you have existing hypoglycemic issues you need to work with that too.
Don't even worry about 'nutrients' in veggies. Seriously. You have to eat a metric tonne of broccoli and even then it wouldn't sway as much as having red meat all the time. If you're eating more veggies now then when you had boys, you're already swaying and there is no need to go to extremes. More strict on the LE diet is not better at ALL.
If you find you can't tolerate sweets, then at least up the empty carbs. I do understand that protein is awfully hard to stick to. You can allow yourself a little higher, up to 50-60grams of protein a day, and that might make it easier and stil be LE friendly. I also have eggs a few times a week, it's hearty but not meat and it's fine for the LE diet.
Anyways, you might find that you can't tolerate going too harsh on the LE diet because of your blood sugar issues, and that's ok! You've got to work with what you can manage. But at the very least please make sure you're hitting 1200 especially at your low weight.