Parsing dates in LibreOffice Calc - is there a better/easier way?

You could use some sort of "lookup table" to translate the month names to dates (this solution is based on a solution proposed for the opposite operation - translate numbers to month names)

Just put the month names one after each other into a column on your spreadsheet, and define a named range on those cells (e.g. Monthnames). Now, you can determine the month's number using =MATCH("Dec",Monthnames,0) which results in 12:

With such a table, you could replace the IF statements by a single MATCH call:

=DATEVALUE(CONCATENATE(MID(A2,8,2),"/",MATCH(MID(A2,4,3),Monthnames,0),"/",MID(A2,1,2)))

or on multiple lines:

=DATEVALUE( CONCATENATE( MID(A2,8,2), "/", MATCH( MID(A2,4,3), Monthnames, 0 ), "/", MID(A2,1,2) ) )

The formula above constructs a valid date value from your example strings:

Use MONTH to extract month value with dummy dd, yy values:

=DATEVALUE(CONCATENATE(MID(A2,8,2),"/",MONTH("1"&MID(A2,4,3)&"1"),"/",MID(A2,1,2)))