Hi and welcome to justanswer.
to answer your question;

You are correct about not being able to operate the PIP function with a universal remote , as a matter of fact i haven`t seen one yet that can do it .

So it would mean that the original remote would be the solution.

I have here a few addresses where you can get that remote or a substitute.

I`ll start with your remote part number ; CLU-417UI

You can use that number if you`d like to do your own shopping or you can take a look at the links below;

http://www.replacementremotes.com/HITACHI/Buy-CLU-417UI-CLU417UI-HL00227-TV-Remote-Control.html

And this one;
http://www.newremotecontrol.com/hitachi/catalog_item.php?catnum=HL00227

or this one;
https://remotecontrolwarehouse.com/HITACHI/CLU-417UI.html

Hope this help and you can close this chat from your end with the ACCEPT button if you are satisfied with my answer and have no other questions at this time.

Also, you will receive an email after this chat is closed and there will be a link to get back to me anytime or you can just send a reply here if you have any questions and i will be with you ASAP.

Thank you