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It seems that the handling of the Alignment option is not consistent for all functions using it. Panel for instance seems to support numeric values for this option

Manipulate[
 Panel["\[Times]", ImageSize -> {100, 50}, Alignment -> {x, y}],
 {x, -1, 1},
 {y, -1, 1}
]

while with Grid this is not supported. Knowing this, you could check functions you're interested in with something simple like

SetAttributes[AlignmentTest, HoldAll];
AlignmentTest[func_] := Row[{
   Manipulate[
    Append[func, Alignment -> {x, y}],
    {x, -1, 1},
    {y, -1, 1}
    ],
   Manipulate[
    Append[func, Alignment -> {x, y}],
    {x, {Left, Center, Right}},
    {y, {Bottom, Center, Top}}
    ]
   }]

You see that in many cases numeric values for the Alignment option can be used

AlignmentTest[
 Button["Click Here", Print[10!], ImageSize -> {100, 100}]]

AlignmentTest[
 Manipulate[Plot[Sin[x (1 + a x)], {x, 0, 6}], {a, 0, 2}, 
  ContentSize -> {500, 500}]]

AlignmentTest[
 Grid[{{"\[Times]", "\[Times]", "\[Times]"}, {"\[Times]", "\[Times]", 
    "\[Times]"}}, Frame -> All, ItemSize -> {10, 10}]]

AlignmentTest[Overlay[{Graphics[{Disk[]}], Slider2D[]}, All, 2]]