The install job uses a internal Utility Model. It's internal because at this stage the models have not been created for CA RC/Migrator yet. The actual text of the model can be found on hlq.CDBASRC(RMMODTXT)
It's called MODELDBA as you can see in your sysout
Model ID ===> @DEFAULT
Model Creator ===> MODELDBA
Control of the dataset allocations are difficult because so much is done dynamically that you cannot see in the ssidDDL member for the SNAPSHOT process.
The SNAPSHOT process dynamic allocation process uses model RMMODTXC (CA utilities) or RMMODTXI (IBM utilities). These models can be found in SRC library CDBASRC. The tape unit is hardcoded as CART.
Customization of the TAPE UNIT of CART is difficult with this configuration. We would tend not to recommend editing the RMMODTXC / RMMODTXI members.