I normally fill their hay before I leave for work, when I get home from work, and before bed, as I’m also out for a good proportion of the day. I think they just tend to get more excited about fresh hay too.
Fruit should be only given occasionally as a treat (eg. mine will get a strawberry or a small piece of apple/carrot about once a week – I’m so mean! haha). Also remember that carrot counts as a fruit in this context because of it’s high sugar content.
But leafy green veg should be a staple of their diet, unless they specifically react badly to it. I give mine a bowl of veg (roughly two handfuls) in the morning and evening. This normally consists of at least three of the below: romaine lettuce, mixed leaf lettuce, rocket, spinach, kale, celery, spring greens, coriander, parsley, basil, mint, cauliflower leaves. I have herbs growing in a window box so I can always sprinkle a few of them on top of the lettuce etc that I buy for the week.
If they’re not used to eating veg, you should introduce it slowly in small portions, and only one at a time. Eg, start with a couple of lettuce leaves every day for a week, and if that goes well, add a few coriander sprigs the next week. It sounds like they have had some veg before, so maybe you don’t need to be so cautious. It’s always good to be especially aware when you give them a new veg for the first time though – some veggies cause gas for some buns.
Also, don’t feel bad about them acting starving, it’s totally normal bunny behaviour!