not only would i do it on the same screen, but i would save even more money and use an opaque ink, and skip the white under base.
i buy union ink. i know a lot like ryopaque.
whatever works for you...
in 1 or two jobs alone, the few bucks you spend on getting a quart of the opaque inks, quickly is recouped in time saved by not having to do the white screen.
that white screen is more than just the cost of emulsion.
you have to:
wash it out
tape & prep it
add that press step to each garment
flash before you can do the next color over it.
after the job is done:
time is money. you can't get time back. EVER.
look how much time you spent above, to be able to print on a black shirt. is that time alone worth 20 bucks? what about on the next job?
anytime i have to print on black, i buy those inks in opaque. i do NOT do white under bases unless absolutely necessary.
when i print on lights, i still use those same inks.. with a little auto formula added in to thin them down. they are NOT just for black shirts.