I loved AccuRadio too and was sad to see it was gone. DASH, Radio Paradise and SOMA fm might be adequate substitutes for you.
You can use AirPlay to cast to Roku from the Accuradio app on your iPhone.
That’s what they told me as well. They also indicated they have no plans to update their app at this time or in the near future. It is a shame as they are by far the best radio streaming service out there and in my opinion better than the stations broadcasting over the air. I’d pay them to keep them available especially to get rid of the goofy ads you have to suffer through on their web based app.