I'm curious what weaknesses of shared_ptr you've found. With the addition of weak_ptr and enable_shared_from_this, they're a pretty versatile tool.
I think the best way to really solve the invalid object problem in C++, is to always put sensible default values inside your struct/class definitions, so your code will at least fail without UB (in addition to using asserts liberally to check for index overflow problems, especially in your own containers even in. Release mode.) Zero-initialization is good for most cases, but sometimes you might need to default-initialize your indices to -1.
weak_ptr is really slow, because of the lock instruction generated for each lock(), as well as the added indirection cost. Once you use them all over the place to fix reference cycles, the overhead of using these becomes hard to ignore. Generational indices/references remove all the ref-counting and gives programmers the semantics of weak_ptr without the performance cost (see https://verdagon.dev/blog/generational-references, the details are mostly language-agnostic).