Hi, You can definitely use all the pins.
I understand that the GPIO header supplied by Raspberry Pi in the kit is physically blocking access to the pins but this is just a physical limitation. The HAT is a Raspberry Pi product and designed according to RPi HAT+ specification.
It is RPi decision which GPIO header is included.
So what can you do?
You can buy an extra long GPIO header or something like Raspberry Pi 40 Pin GPIO Extension Header
Quick and dirty solution:
Remove the standoffs in the GPIO header side and push the HAT a bit more to gain access to the pins.
Note
The I2C pins used as part of the HAT+ standard should be used with more caution as they are used on boot to read the EEPROM, check Raspberry Pi documentation about that.