The Earth historical model for this would be Islam.

Islam expanded very quickly in short time not due to any religious fervour as most are led to believe, but because of the demographic tipping point in an unsustainable environment.

Essentially pre-Islamic Arab culture was based on raiding others, killing all males and enlarging one's number of wives. For a long time this was sustained by the usual factors of starvation, epidemics and other factors, but eventually it caught up with them. Muhammad simply recognised the way things were headed and offered the Arab tribes an alternative - raiding others.

The rest of the three centuries of the Islamic Expansion can be described as a series of strategic raids utilising an entire culture, Arabic.

The rules of raiding are very simple - surprise the enemy. Most of the significant Conquest battle victories were achieved using deception, ambush, and simple treason. After a while the reputation started to preceded the Arabs, and those in their path simply submitted. Consolidation, and fracture, came later.

For Aslans to become 'space Arabs', all they would need in the canon is an Aslan Muhammad, but clearly this would have been to politically sensitive in the 1970s America, so a council of tribes was retained (as existed in the Arabian Peninsula).

And there are other similarities than polygamy and prodigious birth rate.

Fundamentalist Islam is a luddite religion, but does not reject modern weaponry. Those committed to fundamental ideals of the Islamic ideology reject any form of secular (Western) education, and leave most household chores to wives, which necessarily includes financial management. Women often also run businesses, but men retain the profits to be spent mostly on status symbols and 'charity' of supporting Islamic institutions and jihad.

Like the Aslan canon, the Islamic society is seemingly a very polite one, until one realises that all men are potentially armed, and any infringement on one's honour is often avenged in blood, for which there is no limit, or scale; entire families may be subjected to revenge for an infringement by a single member of the family.