We can extract information from WordCloud in order to translate a collection of regions so they pack nicely. First I'll create some BoundaryMeshRegions similar to how the glyphs were created by OP:

$letters = Table[BoundaryDiscretizeGraphics[
  Text[Style[c, Italic, FontFamily -> "Times"]], _Text], {c, Alphabet[]}];

n = 30;

BlockRandom[
  glyphs = RandomChoice[$letters, n];
  scales = RandomReal[5, n],
  RandomSeeding -> 1234
];

Plot the word cloud using random orientations:

wc = WordCloud[AssociationThread[glyphs, scales], WordSpacings -> 0,
  WordOrientation -> "Random", RandomSeeding -> 1234]

Notice that the objects aren't quite touching. Luckily when we convert this scene back to a collection of regions, they will seem to be touching. I think this has to do with padding within Inset. Using regions in the beginning rather then just graphics makes it easier to convert the insets into explicit coordinates and avoid padding.

insets = Cases[wc2, _Inset, ?];

insetToReg[mr_, c_, p_, s_] := 
  BoundaryMeshRegion[TransformedRegion[#, 
   TranslationTransform[c - RegionCentroid[BoundingRegion[#]]]], 
    MeshCellStyle -> {1 -> Black, 2 -> RandomColor[Hue[_]]}]& @ RegionResize[mr[[1]], s]

BlockRandom[Show[insetToReg @@@ insets], RandomSeeding -> 1234]

Or if you prefer a region instead of just a visualization:

RegionUnion[insetToReg @@@ insets]

We can do this for polygons too:

BlockRandom[
  polys = 
   Table[BoundaryMeshRegion[#[[FindShortestTour[#][[2]]]], 
       Line[Mod[Range[16], 15, 1]]] &[RandomReal[{0, 1}, {15, 2}]], n];
  scales = RandomReal[{0, 1}, n],
  RandomSeeding -> 1234
  ];
wc = WordCloud[AssociationThread[polys, scales], WordSpacings -> 0, 
   WordOrientation -> "Random", RandomSeeding -> 1234];
BlockRandom[Show[insetToReg @@@ Cases[wc, _Inset, ?]], 
 RandomSeeding -> 1234]