I think even live-updating could be statically typed. Basically the live-update is a collection of functions that map every data type in the old process into the corresponding type in the new process. In the dynamically-typed case, these functions are just the identity. In the statically-typed case, if the new type has a new attribute, your mapping function has to define a reasonable default value. If you can't do that, your dynamic live-update would have gone badly anyway.
The main problem with pushing a typechecked live-upgrade in one shot is that you'll need to put a big lock around the distributed system (A non-upgraded node messaging an upgraded one would be fine, because the upgraded one knows the conversion function, but what happens in reverse scenario?)
It could be done without a big lock by splitting into three steps:
1) Push an upgrade that changes the types and adds the conversion functions. The valid type is the union of the old type and the new type. Wait until all nodes complete the upgrade.
2) Push an upgrade that instructs the nodes to convert their data and start using the new types by default. Wait until all nodes complete the upgrade.
3) Push an upgrade that removes the old types and conversion functions.
The difference is that attempting to add code to a live system that mishandled an input (either from a non-upgraded node or an upgraded one) would result in a type-error and reject the upgrade.
You could still use Erlang's crashing and supervisor technique, but you would have the additional benefit of using static typing across a distributed system (where each node may or may not have received the upgrade yet).