Can turning up the temperature of a water heater damage it?
The usual remarks about the safety of scalding water anywhere in your system go here.

Physics says the life of your tank will decrease, but not enough for you to notice.

Everything else being equal, hot water has a slightly higher pressure, but expansion tanks are there to deal with that very problem.

The one place you might notice a difference is in energy use. Water in the heater will cool faster when it is hotter. But as worst the difference will be a few dollars a month.

If you are going to pay someone to put in the tempering valve, then it is likely worth changing the tank at the same time.
A bigger tank is the right answer in the long run. The efficiency of the new tank will be higher. The water will last even longer with a bigger heater and tempering valve. I guess it depends on how long you think your current heater will last.

If you sweat your own pipes, I would say stay with your current heater until it is old enough to replace.