Hello,
The reason why the electrode lead wires (not in tungsten, but in soft iron or nickel-iron) melted is most probably the type of ballast employed to run the fluorescent lamp. In the US, it is know that autoleak transformer 'rapid' or 'instant start' type of ballast can cause complete meltdown of fluorescent lamp electrodes and stems at the end of life.
The underlying reason is the efficiency of electron emission by the cathodes. In new lamps, with undamaged electrodes, the amount of energy required to reach a given lamp current is minimal. This leads to a voltage drop in front of the cathode that is in the range of the ionization potential of mercury (i.e. ~10V), and a dissipated power of Ix10 watt in front of the electrode, where I is the lamp current.
When the lamp is aged and its cathodes worn out, the energy required to extract a given current I is much larger, and the voltage in front of the cathode can reach 50 to 100V. If in Europe the series choke and 230V mains does not allow both a high current and high cathode voltage drop, this situation is however different with autoleak ballasts used in the US. with the latter equipment, the dissipated power in front of the cathode can increase significantly over time. So much in fact that the metal and glass parts of the lamps can melt in the vicinity of the cathodes.
If the ballast in your floodlight is not ferromagnetic, then the cause might be a cheap constant-current electronic ballast. As far as I know, Lights of America is not well known for the oustdanding quality of its products.
Max