OP, my brother is on dialysis and brings his supplies to WDW also. He has A LOT of boxes for his 5-7 night trips. He takes the 2 boxes/bags he uses to the trash in the AM or in the evening before he starts his cycle again.
Coffee, we bring our own (Community coffee drinkers) but we have purchased a smaller Keurig that we may start bringing. Housekeeping will give you more coffee and towels. We called one day and they sent up so many towels! We were in a studio a couple of weeks ago, so no washer and dryer. If we have a washer and dryer then I will start a load when we wake up-switch them over and fold them up when we get back from the park.
My brother has been on dialysis for many years and goes to WDW at least twice a year. They drive from Gulfport but I know the company he uses for supplies will ship them to the resort.