Mitigation of dead zones when applying circular polarized antenna
I'm not 100% certain, but I would say "no, transmitting circular polarization inside conductive enclosure does not reduce the amount of areas where linearly polarized field is  zero compared to linearly polarized transmit antenna". Here is my reasoning and assumptions for you to check:


The transmitting RHCP antenna can be divided into to orthogonal LP antennas with \$90^\circ\$ phase shift.
These two antennas could be electric dipoles, even though the tag RFID suggests that an inductive coupling could take place. For traveling waves the magnetic field just tags along.
Adding a second transmit antenna does not increase the total power transmitted.
I assume that the box is electrically large (not much smaller than the wavelength) so that the waves "fit in" your box.
The waves from the two LP antennas travel originally independently of each others, but can, due to reflections, happen to have same polarization (direction of electric field). 
The destructive interference happens when two reflections meet at the same point with same polarization but with opposite phase.
The probability of this destructive interference is not affected by how many "original" transmit antennas you have in your system. Thus the dead zones happen just as often with both RHCP and LP polarizations.