I have to say that I do not think there are good alternatives for unit tests.
Your gripe with them so far is that they did not catch mistakes and slowed down development, right?
I do not think any testing approach will prevent programmers from making mistakes, instead you should focus on writing simple, SOLID methods that are easily unit-tested and then supplement with contract tests as explained in Integrated Tests Are A Scam.
As for slowing down development. How come? Normally when you have an API and tests for it, it should only grow in capabilities. If you have changes that require rewriting half the suite, the tests must be bad (sorry!), probably coupled to implementation details, not behavior.
As counter intuitive as it may seem, the answer to your plight is more, better unit tests, not less, and not something else.
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