A PDF MediaBox is represented by four parameters: x,y of the lower left corner, and x,y of the upper right corner (with 0,0 being located at the bottom left of the page).  And $page->mediabox(62/mm, 100/mm) is a short form of saying $page->mediabox(0, 0, 62/mm, 100/mm).

If you need to reduce the MediaBox at its bottom end, you don't want the lower left corner to be 0,0, so you have to use the four argument version of $page->mediabox().

                              62mm,100mm
         ---------------------
        |                     |
        |   This is your      |
        |                     |
        |   textblock         |
        |                     |
        |   foo bar baz       |
        |                     |
        |   end.              |
        |                     |
 0,$ypos|.....................|
        |                     |
        |                     |
        |                     |
        |                     |
         ---------------------
      0,0
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In other words, if I'm understanding your requirements correctly, all you need is

...
my ($endw, $ypos) = $tb->apply;

$page->mediabox(0, $ypos,  62/mm, 100/mm);    # <---

$pdf->save;
$pdf->end;
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(AFAICT, $ypos - as returned by $tb->apply() - is the current y-position (cursor) after the block has been rendered, i.e. your y-coordinate of the lower left corner.)

Update: just tested it, and it works fine for me.