I built a table very similar to this table you are talking about. The original design is from design within reach. The way I designed mine was with solid lumber 8 qtr and from what could decifer from looking many times at the table on line was that they use 4 qtr laminated together and then opposing lap joints where the three pieces come together for an individual leg. Like you I wanted m&t joints instead so there were minimal changes in grain. My first step was to make a template from mdf so I could determine where those joints should be in order to get the most stability and strength that also determined the angles where the joinery would be.
In terms of how the legs join the center rail it was actually a lot more simple than one can imagine I used flush mount hanger brackets recessed into the rail and flush on the leg to keep them together with seeing any hardware. I could go on and on but I will let you decide how yours should look message me if you have questions