There are a few more potential candidates that to some degree match the description. A number of VTVL SSTO designs are shown here:
http://www.astronautix.com/lvfam/vtovl.htm
Note for example the NAA air augmented VTVL SSTO:
http://www.astronautix.com/lvs/norvtovl.htm
Detko's ATV is on the small side and fairly slender, but is pretty much a pure cone with a ring of rocket engines:
http://www.astronautix.com/lvs/atv.htm
The Gomersall SSTO that Scott features on his site is perhaps another potential suspect:
http://www.up-ship.com/drawndoc/drawndocspaceshuttle.htm
Koelle's Neptun is another possibility, even though it's a three stage design for lunar missions:
http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf
While it doesn't match the timeframe and cargo mission, shapewise the Kankoh Maru might fit the bill:
http://www.astronautix.com/lvs/kanhmaru.htm
http://www.irs.uni-stuttgart.de/institut/mitarbeiter/laufer/LBQ/LBQ-Report2005.pdf
The same is true for Gary Hudson's Phoenix designs:
http://www.astronautix.com/lvs/phoenixc.htm
http://www.1000planets.com/papers/phoenix-history.pdf
The AAS paper PDF also has a VTVL SSTO concept evolution tree that shows a few more possible matches, like Ehricke's Nexus, the already mentioned SERV, the SSX/X-Rocket, and General Dynamics' Millenium Express:
http://www.spacefuture.com/archive/single_stage_to_orbit_vertical_takeoff_and_landing_concept_technology_challenges.shtml
There is also a picture showing a 'family portrait' of different VTVL SSTOs that gives a good impression of comparative sizes of some of these vehicles. As far as I can tell, the original source of that illustration is this article:
Hoeser, S. J., "Technology Readiness Review of the SpaceShip Experimental (SSX)", Journal of Practical Applications in Space, Vol. 1, No. 2, Winter 1990, pp. 37-49.
It is however also shown on page 55 of 'Halfway to Anywhere' by G. Harry Stine, and Dietrich Koelle used it in his AIAA paper "Options for a next generation European launch system", AIAA-1993-4128, as well as his TransCost 7.2 Handbook of Cost Engineering for Space Transportation.
I tried to include it in this post, but unfortunately neither an "Additional Options" nor an "Attach" button were visible when I drafted this post.
Hope this helps,
Martin