There's now a good alternative, which is to use AWS function URLs, which have no timeout (other than the lamdba itself). To quote from the AWS announcement (April 2022),
...sometimes all you need is a simple way to configure an HTTPS
endpoint in front of your function without having to learn, configure,
and operate additional services besides Lambda. For example, you might
need to implement a webhook handler or a simple form validator that
runs within an individual Lambda function.
Sure, it's simple - but its big value here is that it doesn't time out.
You just mark your lambda as requiring a function URL - either through the console or CLI or other build process - and AWS creates one, which then stays constant even as you update the function.
Here's the documentation: https://docs.aws.amazon.com/lambda/latest/dg/lambda-urls.html