So after having the same issue with not being able to adjust height in text box, Width adjustment is fine but height never adjusted with the above suggestions (at least for me), I was finally able to take make it happen. As mentioned above, the issue appeared to be centered around a default font size setting in my text box and the behavior of the text box auto sizing around it. The default font size was tiny. Hence why trying to force the height or even turn off autosizing failed to fix the issue for me.
Set the Font properties to the size of your liking and then height change will kick in around the FONT size, automatically. You can still manually set your text box width. Below is snippet I added that worked for me.
$textBox = New-Object System.Windows.Forms.TextBox
$textBox.Location = New-Object System.Drawing.Point(60,300)
$textBox.Size = New-Object System.Drawing.Size(600,80)
$textBox.Font = New-Object System.Drawing.Font("Times New Roman",18,[System.Drawing.FontStyle]::Regular)
$textBox.Form.Font = $textbox.Font
Please note the Height value in '$textBox.Size = New-Object System.Drawing.Size(600,80)' is being ignored and the FONT size is actually controlling the height of the text box by autosizing around that font size.