Punk-eeek would seem to be compatible mostly with creationism if Creation were, in fact, done by something like a research team or a product design department. One form of life is created and set in place and allowed to develop over time until that type is seen to be less than optimal for the terms of the experiment, so in a short period of time that system is eradicated or knocked back and a new design or set of designs is put into place, etc. DOS gets replaced by windows. Perhaps Earth is a bell jar?
The original creation of the RNA/DNA system appears obviously to be the work of a single pair of hands (God's). Nonetheless when you get to some point in the near pre-history of this planet, the picture changes; the engineering and re-engineering of complex life forms appears to have become a cottage industry with more than one pair of hands involved. There is no reasonable way to picture a well-intentioned God creating biting flies, ticks, chiggers, or disease organisms or any of the myriad creatures of Pandora's box. Likewise there is no reasonable way to picture God needing to go through 100 species of horses or elephants to get to the one he wanted.
Sounds like you’re describing intelligent design. A Creator making one form of life, then after a while making another form of life that is more advanced.
I think computers would be a good example. Every new product cycle has something faster and more powerful than the previous cycle.