Java (the language) should just drop the notion of checked exceptions. It would be fully backward compatible as the checked/unchecked distinction is a language feature not a JVM one.
They simply don't work with Stream and cause abstraction leaks everywhere (e.g. you have to handle IOExpection for operations on StringWriter). It obfuscates flow control.
Anyway the problem with Optional is not going to be fixed by renaming API methods and fiddling like this (sorry to be harsh). The reason Optional is broken is because there is so much legacy APIs which use null to represent "no result" and until all of these APIs are changed/deprecated, then Optional will never be a very useful tool.
As others have commented, the correct solution would be to ditch Optional completely along with the mass of flavors of @Nullable, @NotNull, etc that everyone uses along with having to use package_info.java everywhere and just make "nullability" part of the type system.
Kotlin got it right here. But it would be a breaking change in Java to make not-nullable the default. They could do it the opposite way to Kotlin - add a marker for "not-nullable" instead of one for "nullable" - e.g. "String!" would be a not-nullable String instead of say "String?" representing a nullable string.