Electrical – Do old fluorescent light bulbs use less electricity

Are there reasons other than what I've mentioned for installing these?

Not really. This was the answer before fluorescent and LED. Places that had a lot of incandescent would save more money using 130V lamps when brightness is not a great factor by saving energy and having to change bulbs less than 120V lamps, like an apartment complex.

Another reason is that when an electrical system is close to being at capacity after all the air conditioners come on in the day and then as the night cooled air conditioners would be turned off and the voltage would spike up for a moment. Sometimes the spike would blow the bulbs. Now with updates power companies give better power and spikes are not that bad anymore.

If you really want to use 130V lamps, then on the halogen PAR lamps you might pick a beam spread that suits your task better. Area lighting would be floods or wide floods but task areas, like for reading or hobbies you might want narrow floods or spots. The tighter the beam the more lumens you get.

Both the voltage and temperature could be culprits here - many bulbs are sensitive to overvoltage.

If you are going with LED bulbs, you usually have a wider acceptable voltage range, but you should be able to get the max-voltage info before you buy.

Additionally, LED's have very low heat output, so will be just fine in the enclosures.

So I'd say the problem will be solved by getting LED bulbs (just check that max-voltage on the spec first) - these will last so much longer.

Alternatively, If you are handy with electrics, have a look at the power supply circuit and see if you can reduce the voltage. Are all the bulbs in series? If so, adding a power resistor will drop the voltage (at the expense of some heat generated across the resistor). If the bulbs are in parallel, you'd need to see if there is a voltage control on the power supply itself.