Sorry, didn't understand this chain..
On a side note : I know you may not like this suggestion, but if there is a possibility of getting optical / co-axial out from your PC, then consider any used AVR from OLX in your city (or) try scouting from a local FM.. You may get it for slightly more than your budget (7K) max, with (or) without a remote..
Ex : This ad from OLX - https://www.olx.in/item/yamaha-6-1-working-condition-no-remote-ID1lRr6H.html#73794d9c32
With an AVR and the speakers you have, integrating sub-woofer is just a piece of cake.. You may not use the surrounds.. But eases a lot of your problems and flexible 2/3.1..
Only down side is there is a huge amp on the desk or some where near it powering two tiny speakers But it would outperform the cheaper suggestions.