environment to balance a table in a multicol

I’d like an environment that balances a table in a multicol environment.

By this I mean I’d like to have potentially long tabular-like data
that automatically breaks to another column of a roughly equal number of rows.

like so, automatically breaking after row 3, for a 2 column tabular, into a 2 column multicol
(artist’s rendition)

lipsum lipsum lipsum lipsum lipsum

    row1 col2        row4 col2
    row2 col2        row5 col2
    row3 col2

lipsum lipsum lipsum lipsum lipsum

Additionally, I was looking to use xparse and a multicol to do this,
in order to pass the number of columns to use through the custom environment down to multicols.

Additionally, I was looking to use the book class and showframe package.

I’ve tried two solutions:

solution A, long table

This answer produces the correct output but not when I wrap it in an environment:

Balancing long table inside multicol in LaTeX

I’ve tried two fixes:

solution A, fix 1: replace the vbox{ and } with bgroupand egroup

Attempt no. 1 results in misaligned columns, and these errors:

• Undefined control sequence. begin{myenvironment}
• Package longtable Error: longtable not in 1-column mode.
• Undefined control sequence. end{myenvironment}
• misaligned columns
• @numberne appears in the columns

documentclass[]{book}
usepackage{showframe}
usepackage[]{geometry}
usepackage{longtable}
usepackage{multicol}
usepackage{xparse}

newsaveboxltmcbox

defshortlipsum{par Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.par}

newcounter{entryno}
setcounter{entryno}{1}
deftabline{Test & thevalue{entryno} & Descriptionaddtocounter{entryno}{1}}
deftablines{tablinetablinetablinetablinetabline}

NewDocumentEnvironment{myenvironment}{O{2}}
{
    begin{multicols}{#1}
    setboxltmcboxvboxbgroup
    makeatlettercol@number@ne
    begin{longtable}{|l|l|l|}
}
{
    makeatlettercol@number@ne
    end{longtable}
    unskip
    unpenalty
    unpenalty
    egroupunvboxltmcbox
    end{multicols}
}

begin{document}

This works great!
shortlipsum
begin{multicols}{2}
    shortlipsum
    medskip
    setboxltmcboxvbox{
        makeatlettercol@number@ne
        begin{longtable}{|l|l|l|}
            tablinestablinestablinestablinestablinestablines
        end{longtable}
        unskip
        unpenalty
        unpenalty
    }
    unvboxltmcbox
    medskip
    shortlipsum
end{multicols}

shortlipsum
par

This does not work!
begin{myenvironment}
tablinestablinestablinestablinestablinestablines
end{myenvironment}
shortlipsum

end{document}

solution A, fix 2: replace the vbox{ and } with begingroup and endgroup

Attempt no. 2 results in a loss of output past the first shortlipsum and:

• Missing { inserted. begin{myenvironment}
• Undefined control sequence. begin{myenvironment}
• Package longtable Error: longtable not in 1-column mode.
• Undefined control sequence. end{myenvironment}
• Missing } inserted. end{myenvironment}

documentclass[]{book}
usepackage{showframe}
usepackage[]{geometry}
usepackage{longtable}
usepackage{multicol}
usepackage{xparse}

newsaveboxltmcbox

defshortlipsum{par Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.par}

newcounter{entryno}
setcounter{entryno}{1}
deftabline{Test & thevalue{entryno} & Descriptionaddtocounter{entryno}{1}}
deftablines{tablinetablinetablinetablinetabline}

NewDocumentEnvironment{myenvironment}{O{2}}
{
    begin{multicols}{#1}
    setboxltmcboxvboxbegingroup
    makeatlettercol@number@ne
    begin{longtable}{|l|l|l|}
}
{
    makeatlettercol@number@ne
    end{longtable}
    unskip
    unpenalty
    unpenalty
    endgroupunvboxltmcbox
    end{multicols}
}

begin{document}

This works great!
shortlipsum
begin{multicols}{2}
    shortlipsum
    medskip
    setboxltmcboxvbox{
        makeatlettercol@number@ne
        begin{longtable}{|l|l|l|}
            tablinestablinestablinestablinestablinestablines
        end{longtable}
        unskip
        unpenalty
        unpenalty
    }
    unvboxltmcbox
    medskip
    shortlipsum
end{multicols}

shortlipsum
par

This does not work!
begin{myenvironment}
tablinestablinestablinestablinestablinestablines
end{myenvironment}
shortlipsum

end{document}

solution B, pseudo-nested longtable w/ savebox

This answer also produces what I want, but I couldn’t get it to align with the text.

balanced longtables, multicol and page breaks

I’ve tried:

solution B, fix 1: wrap the commands in an env and remove the table, and that works great!

However…

That works great until I add the showframe package and I get:

• Missing } inserted. begin{myenvironment}3
• Extra }, or forgotten endgroup{myenvironment}
• added space under the longtable

documentclass[]{book}
%usepackage{showframe}
usepackage{longtable}
usepackage{multicol}
usepackage{lipsum}
usepackage{capt-of}
usepackage{xparse}

defshortlipsum{par Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.par}

newcounter{entryno}
setcounter{entryno}{1}
deftabline{Test & thevalue{entryno} & Descriptionaddtocounter{entryno}{1}}
deftablines{tablinetablinetablinetablinetabline}

makeatletter
newsaveboxltmcbox
newsaveboxxxbox
newenvironment{multicolslongtable}[1]{
    setboxltmcboxvboxbgroup
    col@number@ne
    begin{longtable}{#1}
}
{
    end{longtable}
    unskip
    unpenalty
    unpenaltyegroup
    unvboxltmcbox
}
makeatother

NewDocumentEnvironment{myenvironment}{O{2}}
{
    saveboxxxboxbgroup
    begin{minipage}{textwidth}
    begin{multicols}{#1}
    begin{multicolslongtable}{| l | l | l |}
}
{
    end{multicolslongtable}
    end{multicols}
    end{minipage}
    egroup
    begin{multicols}{#1}
        useboxxxbox
    end{multicols}
}


begin{document}

shortlipsum

begin{myenvironment}[2]
tablinestablinestablinestablinestablinestablines
end{myenvironment}

shortlipsum

end{document}

% environment to balance a table in a multicol

documentclass[]{book}
usepackage[showframe]{geometry}
usepackage{longtable}
usepackage{multicol}
usepackage{lipsum}
usepackage{xparse}


% helpers for the test
defshortlipsum{par Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.par}
newcounter{entryno}
setcounter{entryno}{1}
deftabline{Test & thevalue{entryno} & Descriptionaddtocounter{entryno}{1}}
deftablines{tablinetablinetablinetablinetablinetablinetablinetablinetabline}


% box for a multi column long table
% SEE https://tex.stackexchange.com/questions/161827/balanced-longtables-multicol-and-page-breaks
makeatletter
newsaveboxltmcbox
newsaveboxxxbox
newenvironment{multicolslongtable}[1]{
    setboxltmcboxvboxbgroup
    col@number@ne
    begin{longtable}{#1}
}
{
    end{longtable}
    unskip
    unpenalty
    unpenaltyegroup
    unvboxltmcbox
}
makeatother


% environment to accept table input and produce multicol
NewDocumentEnvironment{myenvironment}{O{2}}
{
    saveboxxxboxbgroup
    begin{minipage}{textwidth}
    begin{multicols}{#1}
    begin{multicolslongtable}{| l | l | l |}
}
{
    end{multicolslongtable}
    end{multicols}
    end{minipage}
    egroup
    begin{multicols}{#1}
        centering
        useboxxxbox
    end{multicols}
}


% patch multicols to allow for one column
% SEE https://tex.stackexchange.com/questions/233866/one-column-multicol-environment
letmulticolmulticolsmulticols
letendmulticolmulticolsendmulticols
RenewDocumentEnvironment{multicols}{mO{}}
{%
    ifnum#1=1
    #2%
    else % More than 1 column
    multicolmulticols{#1}[#2]
    fi
}
{%
    ifnum#1=1
    else % More than 1 column
    endmulticolmulticols
    fi
}


begin{document}

section{one column}
shortlipsum
begin{myenvironment}[1]
tablines
end{myenvironment}
shortlipsum

section{two column}
shortlipsum
begin{myenvironment}
    tablines
end{myenvironment}
shortlipsum

section{three column}
shortlipsum
begin{myenvironment}[3]
    tablines
end{myenvironment}
shortlipsum

end{document}