There's a certain irony in routing through the Azores' sleepy volcanic gateway on a lie-flat seat designed for transatlantic royalty, but that's precisely the charm of this itinerary. There is no nonstop service between Indianapolis and Ponta Delgada, so business class from Indianapolis to Ponta Delgada requires a connection—typically through Boston, New York-JFK, or a European hub like Lisbon, depending on which of the three major US carriers you choose. Delta, American, and United all serve this corridor via partner and codeshare arrangements, and the most comfortable routings I've flown pair a domestic first-class hop out of IND with a widebody business cabin across the Atlantic—think Delta One suites on an A330 or A350 out of JFK, or American's Flagship Business on a 777 via Philadelphia. United passengers should aim for Polaris-equipped 767s or 777s out of Newark, which offer more consistent lie-flat configurations than some of their older aircraft still flying secondary Atlantic routes.
Having connected through JFK and Boston multiple times en route to the Azores, my strongest insider tip is this: build in at least a 90-minute buffer at your connecting hub during winter months, since Ponta Delgada's approach is notoriously wind-sensitive, and delays cascade backward into missed connections more often than published on-time stats suggest. Logan is actually the more reliable gateway of the two for Azores connections thanks to shorter taxi times and less congestion than JFK's Terminal 4 during peak transatlantic banks. If you're connecting through Lisbon instead, TAP's partnership with these three US carriers can open up creative routings, though you'll want to confirm your business class hard product before booking, as regional TAP equipment sometimes downgrades the experience.
Seasonality matters enormously here: this is a leisure-driven route tied to Azorean tourism and diaspora travel, so January through March and October into November consistently offer the softest business class fares, well before the summer surge when Boston-area Portuguese communities flood the route. Given how thinly these premium cabins are allocated on a route this niche, I'd strongly recommend setting up fare alerts rather than checking manually—award space and discounted business fares here tend to appear in short, unpredictable windows.