>When a Tap+Hold is done, and moving up or down, on iPhone Safari, the default behavior is to move the Web page entirely up or down a little bit so we can see some white background over the page limit into both directions. Is there a way to bypass that behavior and have the regular page scrolling instead?

That would be called the bounce effect.

To disable that on IOS Safari, the following may be used:

body, html
{
   position: fixed;
   width: 100%;
}