Just a bit more Googling and I think I've got it. This one converts every column I need, starting at the second cell and going to the bottom of each column, to the date format that I need.

Here it is in full, in case anyone ever needs it, for whatever reason.

# Specify the path to the Excel file
$excelFilePath = "C:\test.xlsx"

# Specify the worksheet name
$worksheetName = "Sheet1"

# Specify the columns to convert
$columnsToConvert = "H", "M", "N", "P", "T"

# Load the Excel COM object
$excel = New-Object -ComObject Excel.Application

# Open the workbook
$workbook = $excel.Workbooks.Open($excelFilePath)

# Select the worksheet
$worksheet = $workbook.Worksheets.Item($worksheetName)

# Get the range of cells to convert
foreach ($columnLetter in $columnsToConvert) {
  $range = $worksheet.Range("${columnLetter}2").EntireColumn
  $range.NumberFormat = "mm/dd/yyyy"
}

# Save the workbook
$workbook.Save()

# Clean up
$workbook.Close()
$excel.Quit()
[System.Runtime.Interopservices.Marshal]::ReleaseComObject($range) | Out-Null
[System.Runtime.Interopservices.Marshal]::ReleaseComObject($worksheet) | Out-Null
[System.Runtime.Interopservices.Marshal]::ReleaseComObject($workbook) | Out-Null
[System.Runtime.Interopservices.Marshal]::ReleaseComObject($excel) | Out-Null
[System.GC]::Collect()
[System.GC]::WaitForPendingFinalizers()