Hlrd Congrats on your success!
Re your question...About halfway through P1, I needed help with constipation. It went away once I reached my goal and ate normal calories. (I did IP in 2013 for 7 months). Imo,your veggies sound fine, and it's just a side effect of the diet. I used Smooth Moves tea and that got me through it, no problem stopping it after phase off.
Veggies: I ate a big salad everyday. In hindsight, I would have had 2 salads of the free veggies, for bulk. I think your idea to include spinach is a good one, maybe a second salad of lettuce and free vegs (Sorry, I'm not current with P1 protocol--I'm suggesting the ones that are allowed in addition to the 4 cups).
My go-to veggies were broccoli & cauliflower, mostly the broccoli because it is nutrient-dense. I loved steamed broccoli added to IP chicken soup.
I didn't avoid any allowed veggie in particular, just stuck to what was super easy without thinking too much. But there are all sorts of good ideas & recipes if you search the forums here, to keep it interesting. I need my food to be not too interesting or I just want to eat more

. I doubt any particular veg will matter to weight loss if you are choosing the ones on the list and measuring correctly. Looks like what you are doing is working quite well!
Re stalls: I would not worry about stalling by adding the egg white. Keep in mind that as your weight drops, your scale losses will be smaller too. A week or two of same weight does not equal a stall. Sometimes a week with little or no weight loss is also the week that you notice the biggest change in your shape.
Another thing re stalls that is counter intuitive...the diet is so low in calories that the body can react by slowing weight loss. My coach would sometimes advise people to add a packet to get out of a stall, and it worked.
Keep up the great work! Look forward to reading your progress. The forum here has gotten quiet but it picks up now & then.