I once developed a brain tumor model in rats using only the SV40 large T antigen as the oncogenic stimulus. After a relatively very long latency period of 5-12 months about half of the animals developed so-called PNETs (primitive neuroektodermal tumors), i.e. like medulloblastoma and retinoblastoma. The large T antigen was known to bind to and inactivate tumor suppressor gene products, like p53 and the members of the retinoblastoma (RB) family of proteins, pRB and others, not completely identified proteins. Although the large T antigen was able to induce these tumors, the long latency period argued for further mutations in any other genes.
I then wanted to screen human medulloblastomas for point mutations in the p53 tumor suppressor gene - and became the first to detect such a mutation within this type of primary tumor at a low frequency (at the same time the Vogelstein group found a similar mutation, but only in a cell culture, not the primary tumor), but 20 years later the leading researchers now find this to be a very important subtype of children medulloblastomas.
Your question relates to a similar virus and both, small and large T antigens. They seem to influence so many factors in their target cells, that it may be difficult to elucidate all details on their action. The interesting point in my rat brain tumor model is, that all of the developing tumors showed the strinking morphology of PNETs, i.e. no other tumor types developed. And many animal models use a same name of a human tumor type but look and behave very different; Nowadays we know since the Nobel prize 2008 for Harald zur Hausen, how important viruses can also be in humans; therefore your question for a better understanding of all those proteins is still fundamental.