How to get consistent/predictable results from `Alignment` specs within a `Grid` environment?

Question

IME, the results of Alignment specifications within a Grid environment are completely unpredictable.

I give several examples below illustrating this unpredictability.

My questions are:

1. Is there a way to understand these examples that dispels the seeming inconsistency among, and/or between them and the documentation?

2. If the answer to the previous question is "No", how can one get predictable alignment behavior within a Grid object?

---

Example 1a

Note that, despite a specification of Center for vertical alignment in the first column, the items in this column are not centered vertically.

Grid[
  {
    {Item["sine"  , Alignment -> {Right, Center}], Plot[Sin[x], {x, 0, 2 Pi}]},
    {Item["cosine", Alignment -> {Right, Center}], Plot[Cos[x], {x, 0, 2 Pi}]}
  },
  Frame -> All,
  FrameStyle -> Thickness[Tiny]
]

---

Example 1b

In this case, using a numeric (0) instead of symbolic (Center) specification for vertical alignment produces the intended result.

Grid[
  {
    {Item["sine"  , Alignment -> {Right, 0}], Plot[Sin[x], {x, 0, 2 Pi}]},
    {Item["cosine", Alignment -> {Right, 0}], Plot[Cos[x], {x, 0, 2 Pi}]}
  },
  Frame -> All,
  FrameStyle -> Thickness[Tiny]
]

---

Example 1c

Grid[
  {
    {Item["sine"  , Alignment -> {1, 0}], Plot[Sin[x], {x, 0, 2 Pi}]},
    {Item["cosine", Alignment -> {1, 0}], Plot[Cos[x], {x, 0, 2 Pi}]}
  },
  Frame -> All,
  FrameStyle -> Thickness[Tiny]
]

In this case, the numeric alignment specification seems to work only for the vertical alignment.

---

Example 2a

In this case, the numeric alignment specification don't seem to work at all.

Grid[
  Table[Item[{i, j}, Alignment -> {i, j}], {i, -1, 1}, {j, -1, 1}],
  Frame -> All,
  FrameStyle -> Thickness[Tiny],
  ItemSize -> {7, 10}
]

---

Example 2b

In contrast, symbolic specs work fine here.

With[{initial = <|Center -> "C",
                  Left -> "L", Right -> "R",
                  Bottom -> "B", Top -> "T"|>},
  Grid[
       Table[Item[{initial[i], initial[j]}, Alignment -> {i, j}],
             {i, {Left, Center, Right}},
             {j, {Bottom, Center, Top}}],
       Frame -> All,
       FrameStyle -> Thickness[Tiny],
       ItemSize -> {7, 10}
  ]
]