I know what you mean! Swinub, Spheal and Snover still nest, as does Poochyena, so its possible a nest at a local park could help with Ice / Dark types at some point.
Dragon types though... time to release Dialga / Palkia in raids as shinies! or Gible community day, i'd take either haha.
How are people getting on with the quest line for shiny Mew?
I'm 9/30 for Catching a Pokemon 30 days in a row and just have some Ice, Dragon and Dark types to catch. I've a feeling Dragon types might hold me back a while as most of those we're Dratini from Incense during the Kanto event.
19/30 Ice
12/30 Dragon
9/30 Dark
The PCNY Mew for Gen 2 could be shiny: https://bulbapedia.bulbagarden.net/wiki/List_of_Gotta_Catch_'Em_All_event_Pokémon#Shiny_Mew with a 0.5% chance. Although this only became more common knowledge once the distribution hardware was obtained, I do wonder if anyone was actually lucky enough to get one back in 2002.
This Go event is really the first truly legit way most people outside of Japan have of obtaining their own shiny Mew that can be used in current games, so i'm quite excited for this one.