Can we minimise regular expressions using known DFA minimisation algorithms?
You should have asked first what you wanted : your second line.
Why assume that you have to reverse the determinization procedure to
get back to a regular expression. You confused your readers. You might add it as a possible way you imagined to go about it, after you stated what you want, not before.

To find out how to get a RE from a FA, just search the web for :
"convert finite automata to regular expressions". It is an interesting topic.

If you want a "minimal regular expression", just search for that.
But I am not sure what minimal would mean (number of operators used
?).

If you want to find a "minimal NFA" search for that, but I gather it is a
rather difficult problem, still under research.

If you want a "minimal DFA", search for that. It is a well explored
problem.