The power output of the water heaters is the crucial point. The "high performance" heater is 76 kBTU/Hr, while most water heaters only are around 30-40 kBTU/hour. This larger burner allowed the smaller tank to be able to "keep up with the demand" for quite a while. Another reason is because it maybe would be configured to heat to a much higher temperature, and then use the mixing valve that in includes to reduce the temperature to the reasonable level. I'd consider this "cheating" if it is what they are doing, though it is allowed by the government.
I'm guessing that the listing says one person because it is a small tank, and not based on the FHR (which they should have paid more attention to).
I don't think that you are missing anything based on the specs on FHR. But, you do need to pay attention to the size of your natural gas line. You'll need a higher flow rate with this model since it's usage rate is much higher. You also might need to provide more "leaks" in your house (and room containing the water heater) to allow for it to get sufficient air for combustion. This particular model uses air from its surroundings, instead of having a pipe to bring air in from the outside. Insufficient fresh air will generate CO (very bad for living things) and will decrease the water heater's efficiency. Make sure that you have a CO detector installed near the unit, whatever your choice ends up being.
The first hour rate is an odd metric. It measures the number of gallons that can be supplied at above 110 F, with an initial temperature of 135 F. This is very difficult to use in calculations.
I'd approach the calculations as an energy conservation problem. Use the recovery rate to calculate the burner output (1080 kJ/min in this case). Then (ignoring that entropy is gained in the mixing valve and the heat capacity and density of water depends on temperature), decide on what temperature shower you want, and what temperature water you want in the tank. Use the heat capacity of water to calculate the amount of energy stored in the water heater, the energy usage rate (power out), and the burner energy rate (power in). Assuming use of 6 gpm, input water at 7 C, the tank at 75 C, and using water at 38 C, I calculate that you would have about eight minutes of water. With the 55 gallon tank, you'd have about 18 minutes using these assumptions.
Just by looking at the 90F recovery rate, you get about 80 gallons/hour. So, you could use 80/60=1.33 gpm indefinitely (with a rise of 90 F). But, you probably only need a rise from 45 to 100 F for your shower. In this case (55 F rise), you could use about 2.2 gpm indefinitely with this particular burner.
I had this problem once. Is the water flow in your shower controlled by a single knob? If so, then there is an adjustment thingy inside the faucet knob that controls the ratio of hot to cold water. Take the knob off by prying lose the center plastic cap and removing the screw that holds it on. There will be a plastic piece underneath that you can pull out, rotate a little bit toward the hot side, and then push back in. You may have to experiment a little bit to get it where you want it.
Now, it's been a little while since I did this, and I'm pretty sure I didn't have to turn off the water to tear down the faucet to that point, but I just can't remember for sure, so I guess you should turn off the hot and cold water supplying the shower before you take it apart. You can probably find an exploded diagram of your particular faucet online if you can still read the manufacturer's name on it.
This may not fix your problem, but it's a good first step to check before you get too involved with water heaters and pipes just on the principle that it's a 5 minute job and it's free.
Best Answer
You absolutely cannot delay delivering cold water into the tank to replace the hot water output. You have a pressurized tank which must remain full of water to deliver water. If you had an unpressurized water tank which delivered hot water by gravity, you could do this, but you don't have that.
I assume that the cold feed is very cold in Cambridge MA. You may not be starting with a full tank of 130 F water. It could be that the controls on the boiler are set to reduce the number of heating cycles per unit time. Where is the temperature sensor located vertically in the tank?
Some recommendations on the temperature set point of tank water heaters are that it be set at 140 F (60 C) to prevent the growth of legionella bacteria. Other recommendations give 130 F. Does your shower valve have an anti-scald temperature control?