This looks incredible! Any advice on how to turn the ginger, garlic, cilantro, and chilies into a paste without a food processor/mortar and pestle...

per halfpint, a knife (plus salt) makes a great garlic paste. micro-plane or box grater can help break down the garlic & ginger. fine chop herbs & chilies. Let paste sit in covered container overnight to help flavors blend.

Do you by chance have a blender? You didn't add it to the list, so in case you do, they are great for making pastes. Just pulse it and scrape the goodies down to the blades (blender off of course) often until it reaches the right consistency.

Lately, my store has only carried salted Kerrygold butter, so I have been skipping the salt when I cook until the end or whenever it's appropriate to taste.

Could try to make the paste in a blender.

If you don't have access to any electric appliance, you might be make a rough paste with a large knife (like a meat cleaver) or 2. Yes, it will take more time, but you could get a decent, albeit coarser, paste.