OH MY GOD... your number 4 is so accurate its almost a miracle. This is so true, in fact I usually keep some boiling water on hand as I almost NEVER hit my sparge dead on and its usually low.
When you think about these cooler/ice chest designs, their whole function is to hold the temperature at a certain temperature for as long as possible.
The down fall using them for mash tuns is that if you put a certain amount of hot water in the cooler/chest, the first thing it does is absorbs the heat to get up towards that temperature to stabilize. As this occurs the temperature of the water drops as the heat is being pulled into the cooler. This is what is known as the mash tun thermal mass.
When the first real brewing software came out for use of the homebrewer, it was ProMash. In the setup portion of its software under mash systems/evaporation, there is a setting for "mash tun thermal mass" This setting is to adjust what your mash tun adborbs when you do not preheat your cooler, or what ever you may use to make the calculator work right.
From using the software and dialing in the system using this adjustment, you can actual get the strike water calculator to work right without preheating the cooler.
I don't use Beer Smith, but I would think that there may be an adjustable setting like the one used in ProMash for compensating for the thermal mass of the tun used.
If you go on the Beer Smith forum, or email them, they can tell you how to set up the correction factors, if the program does in fact have one?
On the other hand:
Most brewers instead of going through the hassle of getting the software dialed in, just Pre heat the coolers/chests to get the strike water calculator function to work properly. Others just make their proper amount of strike water a lot hotter then needed then stir it into the cooler, and wait for the temperature to drop into the proper range before dough in.
When stepping up in a cooler for mashout or sparge you face the same problem as the cooler/chest will first absorb the heat before raising the temperature.
When using a strike water calculator, you need to know:
The exact temperature and weight of the grist/grain for the batch.
The thermal mass of the mash tun used.
The amount of strike water you will be using.
The desired temperature of your mash
These factors will formulate the temperature needed to hit the strike temps accurately.