ZTCA is a zip-similar that approximates a Zip Codes. Zip's themselves are a bundle of postal delivery routes of which 11% or so are updated every 60 days or so. They are optimized for mail delivery, not statistical purposes. And there are no Zip-ZTCA crosswalk files available commercially that I know of.
Tracts average 3,060 voting age persons which will be easier to match into 20k regions, Block Groups are the next-best option at 1,880 persons compared to a list of zipcodes referenced on Jan 1 of this year, at 8,230 per general delivery Zipcode (excluding PO Boxes and dedicated or delivery-point codes).
Now, I'm saying this with no knowledge of your application. If it is important that you need known zip areas (90210, for example) then you are stuck with Zips or ZCTA and hope you can stich the two regions together.
My opinion; you're going to need to decide on zip, or zip-similar but not both. If your objective is to package a set of boundaries to precise 20k populations then I recommend using something more granulay, like Census Tracts or Block groups..The other advantage from using these smaller regions is that they strictly conform to state and county boundaries.