We design and install radiant floor heating systems for a living.

We start with proper heat load, reviewing and consulting on building specifications that effect comfort and HVAC efficiency.

Next the fuel source is considered. If you have designed that electricity is the fuel of choice, an electric boiler is almost always the answer.

Once you have the right type and size of boiler distribution of the heated water is next.

As part of the heat load "Manual 'J'" process, the indoor design temperature, outdoor design temperature are used to determine the design water temperature and minimum flow characteristics for the boiler and the radiant panel. They may not be the same.

The minimum flow through any particular radiant panel is one of the finer points of hydronic design but keeping in mind that all pumping is parasitic, it is a waste of precious and expensive electricity to pump more than is required to heat the space to the desired room temperature.

"I'm thinking if I get the fluid (water, or ecologically friendly solution) up to 100-150F, I can run it reasonably quickly through one loop to start to warm that small area, then expand to a neighbouring loop, then the loop on the opposite side of loop #1, etc.
Might work, might not,"

Not.

We design radiant floor heating systems in Canada but you also have your very own Canadian Hydronics Council and Register Designers skilled in radiant floor design...http://www.ultimatecomfort.ca/installers2011/CHClist.php?cmd=reset.

you might get, say, one zone to heat up. but If I were you, I would not put any water in any part of the system I was not running. and this water heater will not run even a majority slice of this system. your output is just too low.

I only need a slight bit of warm floor at the entryway

Warm is relative. If you pump the output from that waterheater into your floor, there is no question it will warm up some and become a radiator for the interior of your building. However, there is not enough output to warm the interior up very much. And, I would set the output temperature of the water heater to a lower temperature, rather than higher. No matter what you set it at, it won't be able to make up the load during steady state, so there is no point in trying to hit a higher temperature.