Was there ever an attempt - formal or informal - to reinstitute slavery in the US during the brief Reconstruction Era?

Somewhat. After the 13th Amendment, some proslavery ideologues recapitulated old rationales for slavery and fashioned it with a romanticized image of the antebellum South. A common argument was that slavery benefited the enslaved by bequeathing to them civilization, education, Christianity, family structure, household amenities, and the paternalistic care of the master. The plantation functioned as a de facto "training school" that, advocates argued, suited the nature of African Americans who ostensibly were not fit for freedom. Similar sentiments were expressed by Northern conservatives as well; in the 1870s, some former Copperheads advocated reenslavement as the only viable solution to what was then called "the Negro problem."

So while there was no large scale concerted effort to reinstitute slavery, there were many Americans throughout reconstruction who decried abolition, arguing that it rendered the nation's future uncertain and that returning to the antebellum system was preferable. It is also at this juncture that Lost Cause propaganda proliferated.

​

Were some slaves not freed after the 13th Amendment, due to circumstance or isolation?

Two points comes to mind:

1. Slavery remained legal in Delaware and Kentucky for six months after Juneteenth.

2. Shortly after emancipation, eight states updated their vagrancy laws to allow convict leasing (search the Black Codes) which allowed for the imposition of labor on convicts. Property crimes such as burglary were disproportionately enforced against African Americans. So what you had were penal codes that both exercised social control and siphoned the black population into labor conditions analogous to slavery. This is what led W.E.B. Dubois to write the following in 1935:

"Slavery was not abolished even after the Thirteenth Amendment. There were four million freedmen and most of them on the same plantation, doing the same work they did before emancipation, except as their work had been interrupted and changed by the upheaval of war. Moreover, they were getting about the same wages and apparently were going to be subject to slave codes modified only in name. There were among them thousands of fugitives in the camps of the soldiers or on the streets of the cities, homeless, sick, and impoverished. They had been freed practically with no land nor money, and, save in exceptional cases, without legal status, and without protection"

It bears noting however that this gets into a murky territory of scholary debate over whether the status of postbellum convicts was indistinguishable from enslavement. They are certainly analogous, but there are important distinctions.