Electric hot water heaters are on the expensive side to run and recovery isn't that good. So if you are looking to get a seperate unit that isn't gas I'll assume it isn't available at your home. If it is then that is a much better option.
You have plans to replace the boiler, if that is true than a new boiler with an indirect water heater will make you plenty of hot water to keep you happy. It was be a waste of money to buy a seperate tank to use only for one year.
It sounds like your coil is showing it's age and just not producing as much hot water as quick as you need. It doesn't help that you added a higher flowing shower head. That will easily cut the length of time you get hot water(water flows from shower faster than the coil can bring it up to temp.)
I wouldn't mess with your aquastat just yet, esp since you seemed to have explained some of the possible culprits.
The plate off the boiler is just a rating and means nothing to anyone who doesn't have the big picture of your whole house.