Both crystal structure and periodic characteristics favor the formulation $\ce{Pb^{II}_2Pb^{IV}O4}$.
Below is a picture of the crystal structure from Wikipedia.
Source
This structure has at least two features that would be consistent with a lead(II,IV) identification:
One third of the lead atoms have higher coordination number (six) to the electronegative oxygen and the rest have lower coordination number (two). The more highly coordinated lead atoms would naturally fit with a higher oxidation state, and $\ce{Pb^{II}_2Pb^{IV}O4}$ fits with the ratio of high to low coordinate lead atoms.
The six-coordinate lead atoms noted above have the same coordination as they do in the pure lead (IV) oxide $\ce{PbO2}$. Note the contrast here with iron, where six-coordination is typical for oxidation states +2 and +3.
In addition, $p$-block elements — unlike transition metals — strongly favor paired-electron structures, which means even-$Z$ elements favor even oxidation states and odd-$Z$ elements favor odd ones. Where the oxidation state has the "wrong" parity it's usually accompanied by homonuclear bonding which allows the electrons to be paired without being polarized (like peroxides with their oxygen-oxygen bond or lead(III) in $\ce{(CH3)3Pb–Pb(CH3)3}$). No such homonuclear bonding is evident in $\ce{Pb3O4}$, so the lead atoms ($Z=82$) would be assigned even oxidation states to fit the general trend.