Changing Address to Rank for the 3 Pack

Doing well on SERP for major keywords for Local SEO except I can't get into the 3 pack because my home address verified with the postcard is too far from what Google considers my city, even though if you lived here you'd consider this well within the "city name".

So, if I change my address on GMB and do the post card change, do I NEED to change ALL my citations?

I'd say the address is the most important thing to rank in the 3 pack. If your address does not include the city name you have practically no chance to rank (unless there is no competition in that city and you are the closest one to it).

So yes, you will need to change the address (a virtual address might be an option here too) and yes, you will need to update all citations - consistent NAP (name - address - phone number) is a major factor in local rankings.