I have the Monitor 17 trim with the separate temp and volume controls. I really like the separate controls.
If you are upgrading your current setup to gain separate temp and volume controls, then your existing single handle cartridge would not suffice so I don't understand why you are asking if you can use the existing 1300 series cartridge.
From what I could read, it sounds like you need the 1700 cartridge RP32104. I'm sure a call to 1-800-345-DELTA would get you an answer. The waranty is only for the original owner but a call might get you a free replacement for your 1300.