When I write regular TLA+, it's usually for things that aren't nearly as "order-dependent".
I'm not sure there is one, but you can start exploring here:
https://en.wikipedia.org/wiki/Category:Formal_specification_...
For TLA+-styled model checking, though, there is Quint: https://quint.sh/docs/why
I agree that spec/implementation conformance checking is also an issue. P has apparently had some success with PObserve for trace validation (checking whether the log of a running system is a valid execution of a P spec) but it is still not a well-known method with these tools in the same way that fuzzing or property-based testing have become. This requires some real product-level thinking to make usable and possibly full ownership of the system execution environment inside a VM or something like that.