While copying to new document and archiving the original one would allow one to see only open quotes or orders, it does not allow for successful quote and lost business statuses.
I would design the archive option so that if you copy a quote or order to invoice then it archives the original as you suggested but also marks that quote as successful. However, an option to archive a quote where you have lost the business (in other words, the client did not accept your quote) is also necessary so that businesses can see what quotes are not being accepted and more importantly address the reason why the quote was not successful.
When you pay an invoice to a supplier or receive money from a client the purchase invoices and sales invoices show a nice paid in full green button in the status column. Likewise an unpaid invoice shows as red button in the status column. I think that successful quotes and unsuccessful quotes and open quotes could have a similar concept - red button for unsuccessful, green button for successful and orange or something else for open quotes/orders and have a status column as well like the sales and purchase invoice view. That way the sales and orders tabs would actually be pretty consistent with the invoice tabs having that status column and it makes it easy to see unsuccessful quotes etc, providing there is an option to view archived quotes obviously.
So I would have default view as open quotes picture in status column. When you click on archive button (or action button), you get two choices - copy to order/invoice and mark quote as successful and archive or second option to archive quote and mark as unsuccessful or lost business. So in a sense its a modification of the existing coding for copying to invoice - but you are just adding coding to archive and set a status. But the program does this anyway when you pay an invoice or receive money (in setting status by changing from red button picture to green button picture).
I think that would work the best as it would make the look of quotes and orders consistent with what you already have in invoice tab and it will address nearly if not all of the issues that most users have requested with regards to pending statuses. I don’t think that its going to be possible to have undending variations of statues on quotes as many people want different things. I would just focus on the most important point which is people only want to see open requests by default. Thats the key issue.