I have been criticised for buying more veg for the hamsters than the humans

Things like cucumber and broccoli will keep for a week in the fridge. It's fine to stick to a couple of staple veg and alternate them. Carrots keep for ages if stored in the fridge. If you can get a small parsley plant in a pot you can keep that in the house growing. A parsley leaf once a week is a nice veg alternative and healthy for them.
It's great he's getting his new cage soon. It's quite important to not clean anything out in his old cage before the move, and to move his old bedding over with him (and ideally at least part of his existing nest and hoard) and move over any other items without cleaning them. A cage move, can be quite a stressful process otherwise. So the idea is to keep their familiar scent which helps them settle in quicker. Otherwise they can be quite stressed and hide away for a couple of weeks and it set taming back as well.
So with a bigger cage you will obviously have a lot more bedding in it, so fill it with new bedding. Then when it comes time to move him in, pop him somewhere safe and take all the old bedding out of his old cage and spread it on top of the new, so it smells familiar. If there isn't that much of it then spread it mainly round the house area.
Also it helps to try and keep the layout similar, in terms of house, wheel etc in similar locations as before. So if the house was on the left and the wheel at the back, it helps to try and recreate that layout/familiar route for them. It isn't always possible to have the layout exactly the same but those little things can help a lot.
If you're using a different house/hide, try and save most of his old nesting area/nesting material and put that inside the new house, along with any hoard you save from the old cage. It doesn't matter if it's all smelly - it will be fine for a couple of weeks while he's settling in, and then you can do the odd bit of spot cleaning if needed, or wipe the wheel.
It's really tempting to put everything in new and clean but can freak out the hamster!
Keeping the odd old item from the old cage helps as well, but he will still enjoy checking out new things in the cage too
If possible, I tend to do a "transition day" as find they settle in a couple of days if you do that. By that I mean, letting him have a play in the new cage, the day before moving him. So for that, you have all the new bedding in and maybe some of the new items you'll be using in the new cage, and take one familiar item (a tunnel eg) from his old cage (for the familiar scent).
And let him have a play and explore in the new cage for an hour or so. Some people find the hamster likes it so much they're tempted to leave them in there, but it helps to then move them back to their old cage overnight, then finish setting up and move the bedding etc across next day for the hamster to move in.
I think this helps a lot because it's not a "cold turkey" move. However lovely the new cage is, they feel safe and familiar in the old cage, so by doing a transition day, they are already familiar with the new cage once they move in (and usually keen!) and have already scent marked it a bit, which helps.
The other tip there is, once you've moved him in, take the old cage out of the room - even if it's just to the bathroom - and clean round that area. They can be quite bothered by the scent of their old cage still nearby. I made mistakes with our first hamster and for ages he kept going over to the area where his old cage was and seeming a bit distressed. When I realised that, I moved it and cleaned the area.
And clean out the old cage straight away after the move, to remove any scent.
It's easier than it sounds!