I was going to recommend the Glenartney, as we absolutely loved it, but they went out of business, I think due to Covid. The Douglas Hotel looks good, but it's pricey. Check Trip Advisor - they're sometimes good for finding something off the beaten path.
You could also try contacting the Brodick TIC, and giving them the dates that you plan to be on Arran. Their telephone number (from the US) is 011 44 1770 303774. Their e-mail address is email@example.com
I've found the TICs in Scotland very helpful in finding accommodation in Scotland, in Tarbert (Harris) and in Stornoway, in particular.
Good luck, and best wishes.