Answering my own question here: It doesn't work.
Switched to ARN-DXB-ICN instead of BLR and booked through Amex Travel for 24h free cancellation.
When booking without a stopover, the EK website offers an immediate upgrade to J during the booking process (67k or so), even though no rewards flights are available for DXB-ICN.
When booking with a stopover, when there is no reward flight available, it was not possible to upgrade, not even to waitlist an upgrade.
When booking with a stopover, when there are rewards flights available (different dates), the EK website only offers to waitlist an upgrade, at considerably higher cost (100k).
When booking with a stopover on the EK website, no upgrade is offered during the booking process, it's apparently just not part of the upgrade flow.
The only thing I didn't try was booking with a stopover on the EK website, and then trying to upgrade afterwards, as the ticket wouldn't have been refundable for free.