Going with a connector that uses crimp contacts --
Plug: 09-50-8091 or CS156-09-LR (generic version of 09-50-3091).
Contacts -- use 08-52-0113
Key (one required) -- 15-04-0297 if using plug 09-50-8091 or 15-04-0219 if using CS156-09-LR or 09-50-3091
You would also need a crimp tool such as a Sargent 1026-CT

All of these can be found here:
https://www.greatplainselectronics.com/default.asp
BUT - my web store shuts down tonight and I'm taking a few days off for R&R.

I believe Todd also has available options:
http://www.bigdaddy-enterprises.com/

And there is Mouser:
www.mouser.com
or Digikey:
www.digikey.com

Now - to go with a crimp type connector, you will need to cut into that green wire and splice in a wire to tie one wire into a crimp contact while still connecting to source and next destination. Bad design by Data East but nothing you can do easily to fix that. There was a thread on doing this on Pinside about a week ago with pictures but cannot find that now.

Other option is to stick with the IDC type plugs you have now. Many of us hate IDC type plugs as they are built for speed of assembly (saves mfr $$$) and not for reliability. But for home use...
Anyways - Pinball Life sells this type plug but for only 22AWG wire. You can find these at www.pinballlife.com. However, it appears that the wire in your photo is larger than 22AWG. You can find the 18AWG plugs at Mouser... but I don't know the part number.