Well Koru membership IS actually quite distinct from the Status Tiers of the Airpoints program...and IS effectively what you are seeking.... a lounge access program.
I assume you actually want a pay-per-entry type of program, given the Koru membership would be rather pricey for "a few times a year"....hence the suggestion by WLGNZ of Priority Pass. That is a particularly good suggestion since you want "any flight/airline" access.... which NO airline club membership will give you.....
As to the dress standards stuff...that's a separate question.... ive never thought the Koru lounges were at all strict....