After much backing and filling trying to make particles behave, I can't get past this last hurdle:

Looking at the Assembly Room, it's obvious that the particle emitter is there. It shows that the colors spec'd are there. [They're even brighter in the Side View]. But when I render the missile in flight, [or still] it looks like a lightsaber hanging out of the back.

[BTW, the rear part of the 'particle exhaust' is just out of the spotlight cone.]