Well, it would be wrong to remove the commas from the first paragraph, since they are actually required.

Thinking more, the reason it feels like there’s a need for commas is probably due to an over-complication of the clause. I think it would help matters to avoid mention of leaders in the Republic, since that’s getting too into the weeds. The important point is that the Republic is helping the Resistance, however fraught that help actually is. On the other hand, it feels like I need more specificity when referring to the New Republic, so I could say that it is armed by the Republic Starfleet, which is basically true. Poe was originally from there, and their ships are undoubtedly New Republic military in origin. It also gives a clear hint as to how it’s so obvious to the First Order that the New Republic is involved - they find Poe’s shiny New Republic X-wing on Jakku. Referencing the starfleet also helps to prime expectation for talk of pilots.

EPISODE VII
THE FORCE AWAKENS

It is a time of despair.
Luke Skywalker, sworn
to reforge the legendary
Jedi Order, has vanished.

Emboldened by the Jedi’s
absence, soldiers of the
evil FIRST ORDER have
risen from the shadows
of an Imperial fortress
to claim supremacy over
all star systems beyond
the fragile New Republic.

Rallying against this evil,
a valiant RESISTANCE
armed in secret by the
New Republic Starfleet
has sent its daring pilots
to find the last Jedi and
restore the light of hope
to the darkening stars….