I have a feeling we're not going to agree in the end, but I'll give it one more go. Only two of the translations refer to the assembly; by far the most common translation is some variation of "all the congregation." But there is at least one unambiguous use of the word "assembly" in the Pentateuch in reference to the entire Israelite people, at Ex 16.3:

The Israelites said to them, "If only we had died by the LORD's hand in Egypt! There we sat around pots of meat and ate all the food we wanted, but you have brought us out into this desert to starve this entire assembly (emphasis added) to death" (NIV).

Further, the laws being communicated would be as applicable—often more applicable—to the common people as to the leaders, with some of the laws being simple reiterations of the Decalogue, as in the Lev 19.3 command that each addressee must respect his mother and father and observe the Sabbath, and 19.4 which forbids idol worship. 19.5-8 gives instructions for the offering of sacrifices from the perspective of the common Israelite. 19.9-10 gives instructions for the conduct of the harvest. 19.11-12 again echoes the Decalogue: do not steal, do not deal falsely, do not lie to one another, do not swear falsely by Yahweh's name.

I'll stop there, since the laws continue in that vein. My point is, even if we accept for argument's sake that God is instructing Moses in Lev 19 to address an assembly of leaders only, the laws themselves are clearly binding upon every Israelite.

In fact, some of the commentaries support the contention that the address was to be given to the leaders of the tribes. Gill's Exposition of the Entire Bible reads:

They could not be all spoke to together, but tribe after tribe, or family after family; or rather the heads of the tribes, and at most the heads of families were convened, and the following instructions were given, to be communicated to their respective tribes and families.

The last clause in that quote is the most important one. The instructions are to be communicated to their respective tribes and families, because those instructions are binding upon all Israelites, not just the leaders. The Jamieson-Fausset-Brown Bible Commentary concurs:

Many of the laws enumerated in this chapter had been previously announced. As they were, however, of a general application, not suited to particular classes, but to the nation at large (emphasis added), so Moses seems, according to divine instructions, to have rehearsed them, perhaps on different occasions and to successive divisions of the people, till "all the congregation of the children of Israel" were taught to know them.