Instead of trying to improve upon determinization techniques for such automata, it might be more fruitful to try to improve these approximation techniques in such a way that more compact automata are produced.
1 because research into finite-state approximation is still of an exploratory and experimental nature, it can be argued that more robust determinization algorithms do still have a role to play: it can be expected that approximation techniques are much easier to define and implement if the resulting automaton is allowed to be nondeterministic and to contain c-moves.