I had a great experience last year getting a delivery from Gooding's (
www.goodings.com), a local supermarket that also delivers.
I chose a delivery because it was very convenient and also a big time-saver --
why would I want to spend precious vacation time inside a strange supermarket where I don't know where anything is stocked???
I chose Gooding's specifically because their delivery policy is VERY convenient. You don't have to schedule a time for the delivery, and you don't need to be in your room. They automatically deliver to your resort's Bell Services (BS). BS then calls your room to see if you're in. If you are, great, they'll be right there. If you're not, they leave you a message to call them, and then they store your groceries for you, even keeping the cold stuff cold (Gooding's separately bags and labels the cold stuff).
The Gooding's website has a quite limited selection, but that doesn't limit your choices. You can order anything they have on their shelves,
except for alcohol. WeGoShop and Garden Grocer CAN and DO deliver alcohol.
OP, you asked if the delivery services are trustworthy. Well, I can say this -- WeGoShop and Garden Grocer are both stand-alone delivery services (they shop at whatever stores you want them to shop at). Their ONLY business is grocery deliveries. They must be good at it or they wouldn't be in business anymore.
And my own personal experience with Gooding's was absolutely wonderful. Roughly half of my order was for specific brands that were not listed on their website but that they stocked in the store -- if you've ever had toddlers and other little ones, you know how brand-loyal and brand-specific they can be. They were great with my deli order, slicing the deli American cheese very thin, as ordered. I ordered about 5 pounds of bananas (for 6 of us over one week), and requested that half be ripe and half be green, so that at the beginning of the week we'd have ripe and ready-to-eat bananas, and by the end of the week we'd have newly-ripened bananas ready to eat, instead of mushy brown ones. They came through with this odd-but-understandable request, also.