While I was gathering data for myself on stat numbers from cards, I realised that card mixing feature can actually use some improvement, as currently it's both clunky and somewhat unoptimal in terms of performance. It is, however, looking similar to what is used in another game I play. So here's my suggestion.
Would you be willing to take a look into Warframe mods system?
As it currently stands, their system allows to convert excess mods into special currency called "endo" (or credits, which is basically a regular money), which then can be infused into mods of your choosing to increase their level. Previously the system used excess mods instead of endo to increase levels, very much like card mixing, where you infuse excess cards of same time to create a higher level card.
Additionally, Warframe system allows to combine several mods to exchange them for one random mod from the massive pull of different mods, rarity chance being somewhat determined by the rarity of mods you combine.
And finally, the sorting system in Warframe also acts differently, in regard that all level 0 mods are grouped together, and the only ones that stand out are the ones that have levels to them, and are usually easier to spot, as you sort them by their "rank". And there is also a search by mod name. Something similar might improve the system significantly (and also possibly resolve, or at very least lessen the issue of when the dolls get their equipped card mixed up when newer cards are introduced into the inventory and/or things get re-sorted). Do not get my word for it, but perhaps try to look into Warframe gameplay footage, and how people make "builds" for their warframes and weapons.
https://wiki.warframe.com/w/Mod - here's the more informative description of what mods are. You might take interest in "Fusion" and "Transmutation" categories.