Organising table sorted by due date

Hi.
We have a spreadsheet we use to keep track of quotes requested by clients. These get entered as they come in and are assigned the next Q number (e.g. Q0002). Since not all clients request their quotes back in the same amount of time the order in which quotes need to be done is not chronological.
I already have a column calculating the days left until the due date and have conditionally formatted the dates to change colour as the due date gets closer. Once the quoted have been finished and sent to the client a status is entered in the status column (e.g. PENDING, WON, LOST, etc)

I was wondering if there was a way to have a second sheet for example that listed all the quotes not yet submitted and sorted them by due date and then sort by time due, and possible another sheet with quotes not yet submitted sorted by the person responsible and then sorted by due date and then by time due.

I have tried getting this to work with pivot tables, but it seemed to require an extra dimension than they could handle. Perhaps I need an extra dimension...

Here is a section of the spreadsheet with some info changed, but all formulas etc still intact.
quotes TEST.xlsx

Thanks in advance.

Thanks! That's looking really good.
The only other things I wanted from it was for it to only show jobs due today or in the future, so once the due date becomes yesterday it no longer shows up in the PT.
Also if there is a status in the status column it doesn't show up (sometimes a quote will be very quick and it will be easier to do there and then because you've just talked to the client on the phone, and if you leave it for 2 weeks you'll have forgotten most of it. This way those quotes won't stick around in the PT).

Thanks.