What happened during times of peace when a large population of relatively unskilled workers returned home and found that they needed to compete with fresh slaves for jobs?

This does not seem, realistically, to have happened. Military recruitment was primarily not among unskilled laborers, who were primarily a feature of the city. Military recruitment well into the Principate was still primarily a rural affair, not an urban one. And while slave labor existed on urban building projects and so forth, the main sources of employment for the urban poor, it was relatively limited. This was partly intentional--Vespasian refused to use a crane mechanism to save labor, out of fear that he would not be able to employ (and feed) so many of the urban poor--but also because in many cases free labor was simply preferable. This extends even to agricultural labor, in which the vast majority of slave labor was employed. Brunt pointed out back in the 60s that people like Cato attest to the preference for free labor in seasonal work, when a great increase in the number of agricultural laborers was needed and landowners were unwilling to purchase additional slaves that would have to be fed and clothed later in the season when their labor would no longer be needed--most likely many of these seasonal workers were part of the urban poor, migrating to the suburban districts with the harvest.