29 sec is the max timeout as of now which works for a majority of use cases. It would be better if you explain what kind of request is it that lasts more than 29 secs. Keep in mind that there might be proxies in the path whose timeout you may not be able to control.
ALB does not have such a limit. It might be a better solution in this case, without knowing anything else. But you won't benefit from rate limiting, throttling, API Keys, etc.
Separating request into POST and then GET polling is an alternative. WebSockets might be another one.
That said, this timeout may or may not be under revision. Even if it is, 29 sec is the limit right now.
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