Below is a single, self-contained Python function that merges the best ideas from all four solutions. It carefully merges continuation lines, detects repeated separator patterns, preserves valid tables unchanged, normalizes column counts, respects leading/trailing pipe style, and performs only minimal fixes if needed:

```python
import re

def fix_invalid_markdown_tables(markdown_text):
    def merge_continuation_lines(lines):
        merged = []
        cur = None
        for ln in lines:
            if '|' in ln:
                if cur is not None: merged.append(cur)
                cur = ln
            elif ln.strip():
                if cur is not None: cur += " " + ln.strip()
                else: cur = ln
            else:
                if cur is not None: merged.append(cur)
                cur = None
                merged.append(ln)
        if cur is not None: merged.append(cur)
        return merged

    def parse_row(line):
        s = line.strip()
        has_lead = s.startswith('|')
        has_tail = s.endswith('|')
        if has_lead: s = s[1:]
        if has_tail: s = s[:-1]
        return [c.strip() for c in s.split('|')]

    def is_separator_cell(cell):
        return re.fullmatch(r':?-{3,}:?', cell.strip()) is not None

    def is_separator_row(cells):
        return all(is_separator_cell(c) for c in cells if c.strip())

    def is_valid_table(lines):
        if len(lines) < 2: return False
        rows = [parse_row(ln) for ln in lines]
        if not is_separator_row(rows[1]): return False
        n = len(rows[0])
        return all(len(r) == n for r in rows)

    def detect_repeated_separators(rows):
        # Returns True if more than half of the odd rows are separator lines
        if len(rows) < 3: return False
        odd_sep_count = sum(is_separator_row(rows[i]) for i in range(1, len(rows), 2))
        return odd_sep_count >= (len(rows) - 1)//2

    def rebuild_row(cells, style):
        s = " | ".join(cells)
        if style[0]: s = "| " + s
        if style[1]: s += " |"
        return s

    def fix_table_block(block):
        merged = merge_continuation_lines(block)
        if len(merged) < 2: return block
        if is_valid_table(merged): return block

        rows_parsed = [parse_row(ln) for ln in merged]
        style = (merged[0].strip().startswith('|'), merged[0].strip().endswith('|'))
        max_cols = max(len(r) for r in rows_parsed)
        sep_flags = [is_separator_row(r) for r in rows_parsed]
        repeated_sep = detect_repeated_separators(rows_parsed)

        def normalize(r):
            if len(r) < max_cols:
                return r + ['']*(max_cols - len(r))
            elif len(r) > max_cols:
                return r[:max_cols-1] + [' '.join(r[max_cols-1:])]
            else:
                return r

        rows_parsed = [normalize(r) for r in rows_parsed]
        fixed = [rows_parsed[0]]
        fixed.append(["---"]*max_cols)
        if repeated_sep:
            i = 1
            while i < len(rows_parsed):
                if sep_flags[i]:
                    i += 1
                    continue
                fixed.append(rows_parsed[i])
                fixed.append(["---"]*max_cols)
                i += 1
        else:
            for i in range(2, len(rows_parsed)):
                if not sep_flags[i]:
                    fixed.append(rows_parsed[i])
        return [rebuild_row(r, style) for r in fixed]

    lines = markdown_text.splitlines()
    out = []
    block = []
    in_table = False
    for line in lines:
        if '|' in line:
            block.append(line)
            in_table = True
        else:
            if in_table:
                out.extend(fix_table_block(block))
                block = []
                in_table = False
            out.append(line)
    if block: out.extend(fix_table_block(block))
    return "\n".join(out)
```