I'm a non-DMU user too, and I was struggling at the beginning (many years ago) to find event components. I don't know what's your level, but for me what works is to send 10 one-man auto missions to low-level places once a day and regular 3-man missions once a day, plus the Island; I found about 500 parts before I started opening boxes and crafting, 5 days after the start of the event.
About the boxes, the components were in Budget Boxes, and I think they were intentionally added to make it more of a bet, in the same way that Trick or Treat boxes contain garbage:
I've been playing since 2012, I'm no stranger to the way the item drops works but I shouldn't have to resort to automating low level missions to get the components to craft even just one of the event items. It's only been a recent trend (as far as I've noticed, since Halloween last year for the EXO suits) that you usually may not get enough components to craft unless you're using DMU or uncrating the components.
Also the crates this event dropped a lot less than previous events, I have two accounts for this game and on both accounts I've only dropped 5 each. The crates aren't advertised as much as a risky gamble as the trick or treat boxes though, the trick or treat boxes have straight up garbage in them. Their 450 x 5 price tag vs the 450 x 10 price tag for skeleton keys kind of show that too.