Try Korean, using Delta miles from MR and/or KE miles from UR if necessary. I see tons of dates where JFK-ICN-CGK has 5x business class seats available using the new Delta award calendar. Do a 5-week flexible dates search using one-way searches to find availability on specific dates (look for 70K options, which is the price of a one-way US-Asia using Delta miles), and then once you find dates that work put them together in a roundtrip search. DPS has fewer options than CGK but there are still a few. The connection in ICN is annoyingly long (10 hours), but given how few other options you are likely to have for this trip, I'd say go for it.

Note that other KE routes from the US are going to be much harder to find 5x seats; it's the tons of business class seats on the A380 from JFK that makes the awards so easy to find on that route. ICN-LAX and ICN-ATL also have a decent amount of 5x days available but I don't see very many for ORD, though if you book far enough in advance you can find space to include a Delta domestic leg to your departing KE port at no additional cost.

You may also be able to find space on Garuda Indonesia's flights from ICN to CGK or DPS, though you would have to call for that, it doesn't display on Delta's website, so I have no idea if they would be likely to have 5 seats on the same flight, but I suspect they might.

You would need 140K * 5 or 700K roundtrip to book 5 tickets using Delta miles. Looks like you have that between Delta and MR.