I wasn't planning on answering my own question, but I've been obsessing about the problem.
This paper https://www.lpi.usra.edu/meetings/marsconcepts2012/pdf/4216.pdf describes a landing with an entry mass of 7200kg, 1900KG of fuel, 5180kg of landed mass and 1000kg of actual payload. Launched by a Delta Heavy variant (it was written in 2012), it left about 7m3 of space remaining. That allows for 1900kG of fuel, given the SuperDraco fuel is on average about 1g/cm3, that's about 2m3 of space refunded, for 9m3.
Wikipedia lists draco as an Isp of 300 (vac) and SuperDraco at 265 (SL), so that translates to between 750-1000m/s of DeltaV to land. Upgrading to a Falcon Heavy gives us a maximum entry mass of 16T ((TMI payload 16.8T, rounded down).
Maintaining the requirement to have 1km/s of DeltaV, that gives a maximum landing mass of 11500KG, 4500KG fuel. The capsule mass was given as 4180KG. Increasing that by 25% (heat shielding, upgraded engines, kerbal paintjob, rounding errors) is 5500KG. 11500KG - 5500KG = 6000KG of payload. Probably 5500KG, because you'd want to have some fuel left over...
Volume wise, we had 9m3 to start. SuperDraco fuel has a density of 1.4 and 0.8 g/cm3, so average that out as water for 6000KG tonnes of fuel is 6m3. So about 3m3 of payload.
So if you don't mind sticking to cargo with an average density above 1.83g/cm3, you have a payload of 5.5T. For less dense payloads, as the fuel requirement decreases, you get more volume reclaimed from fuel. Special case payload, you only brought fuel. 9m3 of volume, 9000KG+5500KG=14,000KG TMI load. Landing mass of 10,000KG. 5500KG for the capsule, or about 4500KG of fuel. Two full payloads would refuel a Red Dragon. That would, assuming Vac Isp of 300, get you 2.7km/s of DeltaV. Or not enough to make Mars orbit at 3.8km/s, but interesting.
Final answer: Between 0-5.5T of payload, with harsh density/volume constraints. Works for machine parts, dissembled machines, food etc - but doesn't allow, under any circumstances, for a manned mission. Would be sufficient for cargo support to a manned mission – which was the intent behind the question.