In my experience short term and long term memory recall speed and accuracy are strongly correlated. It's unlikely someone will be able to swiftly traverse a large long term memory graph, in a manner that would allow you to derive deep insights not just recalling a single piece of information, but have a poor short term memory.

However I do believe long term memory is more robust so if you're in a mentally compromised state, such as having a headache, it will be less affected. So if you have to work through a hard problem on a deadline but have a headache, you can rely on heuristics stored in long term memory rather than deriving everything in short term memory.