As already stated, the types of information asked for in the Census changed over the years, and so did the arrangement of the Census itself. The 1880 Census introduced the numbering of the Enumeration Districts -- this change in arrangement may be why Morse's Unified ED finder only starts with the 1880 Census.
In her article "Plans of Division": Describing the Enumeration Districts of the 1930 Census, before starting her description of the EDs for the 1930 Census, Claire Prechtel-Kluskens writes:
The bureau used the term "minor civil division" to describe the
political subdivision unit below the county level (such as cities,
towns, villages, precincts, and townships), since the name for that
unit varies widely throughout the United States. According to the
general "Instructions for Making Plans of Division," every
incorporated place and unincorporated places with populations of more
than 2,000 were designated separate EDs.
The numbering and arrangement of enumeration districts evolved over time. For the 1790 through 1870 censuses, the EDs were not numbered and consisted of large areas that included many MCDs. For the 1880 through 1920 censuses, each county was divided into numbered EDs.
The US National Archives (NARA) has microfilm of a typescript of the plans of division, published as Descriptions of Census Enumeration Districts, 1830 - 1950 (T1224, 156 rolls). NARA's Document DESCRIPTIONS OF CENSUS ENUMERATION DISTRICTS, 1830-1890 AND 1910-1950 (T1224.pdf) describes the arrangement of the microfilm rolls.
A table of contents for each census year has been provided. The
original volumes are arranged by assigned volume number, beginning
anew with each census year. Within individual volumes the pages are
typically arranged numerically by supervisor's or marshal's district
and thereunder numerically by subdivision or enumeration district.
This arrangement often conforms to an alphabetical arrangement by
county. Major cities are sometimes arranged separately from the
counties. As an aid to the user the 1850 and 1860 volumes, which have
little order in the original, have been filmed out of the original
page sequence so that the states and territories appear on film in
The descriptions for the 1860 Census are on T1224 Roll No. 2; the original page numbers for Missouri are 122-132 (but as noted above, you'll find the state alphabetically in between Mississippi and Nebraska Territory). The microfilm publication T1224 is available at the Family History Library.
The 1860 Census Schedules are on NARA Microfilm M653. Most people are familiar with searching via sites like Ancestry or Heritage Quest, but you can also view the microfilm online, at the Internet Archive, because the Allen County Public Library shared their copy of the census with them.
On his website, genealogist Michael Hait, CG has kindly shared a copy of his document Census Pathfinder and NARA's document M653.pdf which describes the arrangement of the rolls, so we can see that the schedules for Missouri are on rolls 625 (free schedules) and 662 (slave schedules).
Using this information along with the microfilm at the Internet Archive, or by browsing on Ancestry, if a place search fails, you can 'walk through' the microfilm images for Jackson County the old-school way, or by using the actual microfilm at a facility like a NARA regional archive, the Allen County Public Library, or the Family History Library.
Ancestry also has the U.S. Federal Census Mortality Schedules, 1850-1885, but the state of Missouri is not listed in the coverage table on that page.