One tip I learned on here is to distract them by tossing in yet another handful of hay. I thought, "that won't work, they've got tons already" but it totally does work. They all run to the new handful and have a poke and a forage through for the best bits!
Flora is the worst for veggies - she obviously has something in mind when she comes to beg and if I don't offer the 'right' thing she nibbles at it in such a disappointed way that I feel a total failure. I end up offering her a choice like a desperate mum. The others are just delighted with anything - they didn't get that hefty through fussy eating!