Contrary to your claim, $\Lambda_{\rm QCD} \sim 300 \, {\rm MeV}$ is not at the electroweak scale $v=(G_F \sqrt{2})^{-1/2}\simeq 246 \, {\rm GeV}$, instead these energy scales are differing by roughly a factor $10^3$.
The order of magnitude $\sim 1 \, \rm GeV$ of the masses of hadrons like $\rho$, $p$ or $n$ (without heavy quark content) is explained by $\Lambda_{\rm QCD}$, whereas the contributions from the quark masses $m_{u,d}$ to $m_\rho$, $m_p$, $m_n$ are only tiny effects of a few percent. The masses of the pseudoscalar mesons $\pi^\pm, \pi^0$, being Goldstone bosons of spontaneous chiral symmetry breaking in QCD, are even further suppressed, with squared masses $M_\pi^2 =B(m_u+m_d)$, where the factor of proportionality $B$ is related to the quark condensate $\langle 0 |\bar{q} q |0\rangle$.
On the other hand, the scale of electroweak symmetry breaking $v$ determines the masses of the electroweak bosons $W^\pm, \, Z^0$ via
$$
M_W^2=\frac{g^2 v^2}{4}\simeq 80 \, {\rm GeV}, \qquad M_Z^2=\frac{(g^2+g^{\prime \, 2})v^2}{4}\simeq 91 \, \rm GeV, $$
where $g, \, g^\prime$ are the coupling constants of the electroweak gauge group $\rm SU(2) \times U(1)$. At the same time, the masses $m_{ f}$ of the spin $1/2$ fermions $ f= e, \mu,\tau, u, d, c,s, t,b$ are related to the electroweak scale by Yukawa couplings $y_{ f}$ via
$$
m_f=y_f \, v.
$$
The observed large mass hierarchy of the leptons,
$$
m_e\simeq 0.5 \, {\rm MeV}, \quad
m_\mu \simeq 105 \, {\rm MeV}, \quad
m_\tau \simeq 1777 \, {\rm MeV},
$$
and the quarks,
\begin{align}
m_u &\simeq 2 \, {\rm MeV}, \quad m_c \simeq 1.27 \, {\rm GeV}, \quad m_t\simeq 170 \, {\rm GeV}\\[5pt]
m_d &\simeq 4.7 \, {\rm MeV} \quad m_s \simeq 93.5 \, {\rm MeV}, \quad m_b \simeq 4.2 \, {\rm GeV},
\end{align}
ranging over five orders of magnitude, can be accomodated but not explained within the framework of the standard model.
The mass hierarchy problem becomes even more pronounced in view of the neutrinos with masses $m_\nu < 0.8 \, {\rm eV}$. The theoretical description of the experimentally observed neutrino oscillations and the measured mass differences requires an extension of the minimal version of the standard model. In many of these extensions, the seesaw mechanism is employed as an explanation of the smallness of the neutrino masses compared to the masses of their charged leptonic partners.
