would only be able to accomadate around 5A total. I am not fully understanding how the contractor came up with the values for these transformers, or how a 36V secondary would provide the desired 240V at the panel?
The key feature of a 'buck/boost' setup is that the secondary of the transformer is placed in series with the supply voltage, so that the low voltage secondary is added to the high voltage supply, giving a new changed high voltage.
As Wayne described in post 2, only a portion of the total output power is actually 'transformed', so the load on the transformer is only a fraction of what is delivered to the load.
I think there is an error in your original description. You state that 120:36V transformers are being used. My _guess_ is that the secondary is really a dual voltage 18/36V design, wired for 18V. If this is the case, then the transformers would be wired in a wye boost configuration, taking the L-N voltage from 120V to 138V, and giving a 239V L-L.
A transformer kVA rating is based on its use as an isolation transformer, and can be used to calculate the maximum secondary current. The allowed secondary current doesn't change in a boost configuration.
So these transformers have a secondary current capacity of 1500/18 = 83.3A. In the wye boost configuration, 3 of these transformers can supply 83.3A at 239V, or 34.5 kVA (in agreement with Wayne's calculation)
Jon
(NB I've glossed over the way subtractive polarity is used for the buck connection)