Well it depends on who else books them on each cruise. On the cruises I have been on, and checked, there is available rooms for a reasonable time. But I have seen them sell out. Best advice is to book asap.
Twice when I let DCL pick my cabin I got an HA room. Once it was a veranda, once an outside cabin. This was 2 times out of 3 times, all in the last 2 years.
I'm going to say it's a crap-shoot, same as finding an HA room with the accommodations you need at the last minute in WDW. Does DCL have adequate number of rooms? I believe they adhere to ADA regulations, but the % can seem low if there is high demand; same as WDW resorts. FLR and MTO rates typically are very specific categories, not as broad as *GT rates, so that in and of itself will limits HA options further. If you can make-do with a non-HA stateroom, it might be worth the gamble to try for a last-minute offer and request an HA room. But if you absolutely must have an HA room, I honestly wouldn't take the chance.
We booked a last minute trip. My in laws needed a HA room. When the travel agent called and asked about if one was available, they said that they had one, even thought the list of available rooms online didn't show it. My wife and I got a guaranteed family veranda. They didn't assign it until 4 days before the cruise and it was also a HA room.
So my theory is DCL holds some in quiet inventory for people who truly need one. Then release them when they are at the final days of booking. Thus the reason there is a slightly higher chance that when they assign the room it could be a HA stateroom.
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