Food cooking appliances are not permitted in Disney hotel rooms, other than those supplied by Disney (i.e. microwaves and coffee makers). You might want to rethink using a hotlogic and leaving it on when not in the room. You could return from a day in the park to find it has been unplugged and your food uncooked.
Disney will not place an extra fridge in your room but you can request a microwave. They are available on a first come basis and there is no charge. There are also microwaves and toasters in the food court for use by guests. You might want to have a Styrofoam cooler included in your grocery order and just load it up with ice daily to keep your veggies fresh, or place a second grocery order midway thru your stay in order to save space.
I've used Instacart.com and DizzyDolphinDelivery.com to deliver to my DVC resorts in the past. I had to meet the Instacart driver at the lobby entrance because there was alcohol in the order. Dizzy Dolphin left my order with bell services before we arrived and a bell hop brought it to us after we got our room. Of the two, DD was much more familiar with Disney and how to work with them. They were also more expensive. Instacart was less expensive and the level of service all depends on the shopper/driver that gets assigned your order. Both companies book up quickly, so I would arrange delivery no later than a week prior to arrival if using either of them.
Other delivery services include
Amazon Fresh and GardenGrocer.com GG got a black eye on the disboards a few years back and I rarely see it recommended anymore. Amazon seems to do a satisfactory job at Disney. I was unimpressed with it when I tried them at home.
I think cooking...REALLY cooking...in a Value Resort room is going to be challenging. More so if you need to slice, dice or chop a lot of veggies. Counter space is at a premium and the only sink is the bathroom sink.
Most people who "eat in" opt for easy to prepare meals that are not as healthy as you would make at home. But when you're on vacation, you're allowed to let yourself go a little. I admire your intentions of sticking with your 7 veggies a day diet while there. Are low/no sodium canned veggies an option? It would save on refrigerator space and the need to clean and chop them.