Has anyone a working strategy to collect all the card items on the first map?

I didn't manage this run. But I have been thinking ahead for the third run(I assume these quests appear on subsequent play-troughs as well?);
Use a few long-range characters to occupy a few central areas from both entrances. Then use Teleport/Displace to get enough of your long-range/Teleport Skill(goes through walls here)/Double Action Characters to those spots and use them to collect everything. Any short-range characters can be used to occupy/prepare path for the rest of the characters if need be(better have a healthy supply of Teleport stones/Stimulants...).
Once everything is collected, let whoever you left unacted near base enter it so the map ends and the soldiers don't have a chance to act their turn.(Assumes you cleared the rest of map beforehand.)

All those cards are power-ups, so collecting everything is very much worth it (unless your characters are already at max...).