The amp and preamp do not have to be fully balanced to get benefit from XLR cables. While it is true that the simple adaptors that convert XLR to RCA are pretty much worthless, the device linked by @holmz is not a simple adapter. This box includes a transformer which is as effective (if not more so) at eliminating common mode noise as a differential input.
An RCA connection relies on the ground connection for the return current. This connection method was originally developed to connect subsystems in a single console system, where all subsystems were powered by the same connection to the wall outlet. Whenever the components that are connected do not share the same AC connection, you have the potential for a ground loop.
Well designed components minimize this problem by using a combination of diode bridge and resistor between the analog ground and safety ground, but, by necessity, there is still the potential of current flow between these two grounds.
The interconnect and AC connections form a loop. Any electromagnetic waves that are "captured" by this loop will cause a current flow through the loop. The larger the loop, the more this will occur. If the two components are plugged into different AC circuits, the loop can be quite large.
Ground loops doesn't just mean hum (although AC mains radiation is usually the strongest contributor).
The Pro audio industry recognized this problem and adopted balanced connections as the solution. A balanced connection does not rely on a common ground connection between components, so it's possible to use very long cables without the risk of ground loops.
If the preamp XLR connections aren't actually balanced, then using a transformer won't do anything. But most preamps that have XLR outputs will at least use an opamp to create the negative phase signal.
Obviously adding additional circuitry (including the transformer) has it's own disadvantages. So I wouldn't recommend this for a short connection. But long connections such as the OP is proposing will probably benefit.
The connection between the Jensen box and the monoblocks should be kept as short as possible, but these boxes will provide most, if not all, the benefit of having a balanced input on the amp.
I am using a Jensen transformers on the inputs of my DIY 300B SET monoblocks with XLR connections similar length to what the OP is proposing, and they sound fabulous. I also have a pair of Pass XA60.8 monoblocks, and to me and several audiophile friends, the 300B monoblocks with Jensen transformers sound better. So I think these transformers are quite good and don't do much to degrade the sound.