The insert is great but too big for the number of cards, and the HCO box is so pretty that it bugs me keeping them separate. So I ditched the insert and use the top and bottom of the HCO box as trays (it does mean you have to take them out to admire the artwork). I keep the character cards, missions and stickers in them (I have the more-easily obtained second character pack) and find that there is enough room in the rest of the box to wedge (without damaging them) two sets of sleeved cards (in baggies) side by side alongside the HCO box and lid respectively. So it makes for a neat, snug pack that almost makes up for the loss of the original insert, which didn't really accommodate the character and mission cards anyway (what were they thinking?).
Yeah, the insert is ok for cards but there's no place for mission and character cards. I ditched it like you but did the reverse. Cards in Deck Boxes and character and mission cards in ziploc. But i might borrow your idea of using the HCO box for those large cards.