You should be able to tune lower (probably) but without knowing what you're dealing with and with no Theile-Small parameters it's hard to know.
"Modern" speakers haven't changed much except most modern home subwoofers are active and yours may be passive. AVRs don't have a "powered" subwoofer output so most home theater setups have an active subwoofer or a separate amplifier for the bass. And once you have active circuitry, the manufacturer can build-in some frequency-response correction to tame a bump, or to extend the low end a bit. (You can't extend the lows too much with this kind of "trickery" because you run-out of amplifier power and start clipping or risk over-driving and distorting the woofer, etc.)
Paper cones are OK, but is there some kind of compliant surround?
Have you opened the cabinet to see if there is a manufacturer & model number? If so you
might be able to find the specs.
If you want to replace the drivers, and/or add a port or change the port dimensions, you can use
WinISD (free speaker design software) or similar to predict performance. But, you can't use the software to evaluate and compare the existing design without knowing the driver parameters.