SQS limits you further in other ways. For instance, scheduled tasks are capped to 15m (delaySconds knob), so you'll be stuck when implementing the "cancel account if not verified in 7 days" workflow. You'll either reenqueue a message every 15m until its ready (and eat your the SQS costs), or build a bespoke solution only for scheduled tasks using some other store (the database usually) and another polling loop (at a fraction of the quality of any other OSS tool). This is a problem well solved by sidekiq, despite the other drawbacks you mention.
If you wanted to handle this scenario with the serverless AWS stack, my recommendation would be to push records to Dynamo with TTLs and then when they pop have a Lambda push them onto the queue. Would cost almost nothing to do this. If you had 10 million requests a month your Lambda cost would be ~$150 to run this (depending on duration, but just pushing to a queue should be quick). Dynamo would be another ~$50 to run, depending how big your tasks are.
Granted now you need 3 services instead of 1. I personally don't find the maintenance cost particularly high for this architecture, but it does depend on what your team is comfortable with.
I've explored this space pretty thoroughly, including the Dynamo approach you've described. Dynamo does not have a strict guarantee on when items get deleted:
TTL typically deletes expired items within a few days. Depending on the size and activity level of a table, the actual delete operation of an expired item can vary. Because TTL is meant to be a background process, the nature of the capacity used to expire and delete items via TTL is variable (but free of charge). [0]
Because of that limitation, I would not use that approach. Instead I would do Scheduled Lambdas to check for items every 15 minutes in a Serverless Aurora and then add them to SQS with delays.
I've had my eye on this problem for a few years and keep thinking that a simple SaaS that does one-shot scheduled actions would probably be a worthy side project. Not enough to build a company around, but maintenance would be low and there's probably some pricing that would attract enough customers to be sustainable.
Bottom line, there is no silver bullet.