Most mobhead looting tables use this database as source for their textures: https://minecraft-heads.com/
Indeed many servers use the headshop plugin what uses custom heads that will never change their textures, because they do not link to any excisting player account.
In our server it seems they use player heads, what means if the said player for example Snowman_7 decides to change his skin to blood thirsty snowgolem then that will be the looks the dropped head will have as it will change if the owner of the account choose to change it.
Luckily at some point Mojang decided to create a number of accounts with specific skins and it seems that quite few of those accounts are used in our server to provide the skin for the heads dropped. These accounts have names in the format MHF_<Name> . So if you visit
https://minecraft.gamepedia.com/Mob_head you can see a list of the accounts there.
But besides these mobs and blocks that you can find in this list, there are quite few extra accounts with the format of MHF_<Name> that are not created by Mojang, but by some enthusiastic people who saw an opportunity and used it. At this point I can say I am pretty sure that the parrot head that we have on the server is of that origin it means it looks similar, but is not actually the best possible skin for that.
(Then again the Parrot did a way better then the Husk...)So why would I suggest the two names I did?! That's simple they actually look like the SnowGolem, plus for past three years both
Koebasti and
GLaDOS have kept their skins as they are seen now, so it's pretty safe to say that they will probably remain as that for a long time.
As for the drop rate, I agree some mobs in our server should have a way higher chance to drop heads or at least have a possibility to buy a said mobegg from the server shop to increase the chances for the head or to show off in a zoo or some awesome minigame or contraption, simply cause their spawn rates are close to zero, they don't respawn or you can't transport them from one dimension to another due to some technical difficultis [looks at polar bears, vindicators, evoker, elder guardian, shulker, ghast and wither skeletons(I have heard that bringing last two through the nether portal makes them die/go boof)]