The idea here is a cheep and easy way to make a core that is penetrable from all sides.
Here you can see I cut three spots open in a litter bucket with plenty of room in the bottom to hold darts. A fourth is easy to make but I'll explain more later.

Some simple measures and cuts of cardboard here.

Put them in as such and BAM: instant portable cheep core!

MAJOR FLAW: after much testing it is quite the exception if a dart will acctually STAY in the core instead of bouncing out. About one in seven shots stays in. So while this prototype itself is basically useless the idea is sound and could be duplicated with larger objects.
SILVER LINING: cat litter box pannels like the ones I cut out are great alternatives when polycarbonate sheets are overkill!