  We present a faster repumping scheme for strontium magneto-optical traps
operating on the broad ${\mathrm{5s^2} ^1\mathrm{S}_0} - {\mathrm{5s5p}
^1\mathrm{P}_1}$ laser cooling transition. Contrary to existing repumping
schemes, we directly address lost atoms that spontaneously decayed to the
${\mathrm{5s4d} ^1\mathrm{D}_2}$ state, sending them back into the laser
cooling cycle by optical pumping on the ${\mathrm{5s4d} ^1\mathrm{D}_2} -
{\mathrm{5s8p} ^1\mathrm{P}_1}$ transition. We thus avoid the $\sim 100 \,
\mathrm{\mu s}$-slow decay path from ${\mathrm{5s4d} ^1\mathrm{D}_2}$ to the
${\mathrm{5s5p} ^3\mathrm{P}_{1,2}}$ states that is part of other repumping
schemes. Using one low-cost external-cavity diode laser emitting at $448 \,
\mathrm{nm}$, we show our scheme increases the flux out of a 2D magneto-optical
trap by $60 \, \%$ compared to without repumping. Furthermore, we perform
spectroscopy on the ${\mathrm{5s4d} ^1\mathrm{D}_2} - {\mathrm{5s8p}
^1\mathrm{P}_1}$ transition and measure its frequency $\nu_{\mathrm{^{88}Sr}} =
(668917515.3 \pm 4.0 \pm 25) \, \mathrm{MHz}$. We also measure the frequency
shifts between the four stable isotopes of strontium and infer the specific
mass and field shift factors, $\delta \nu_\text{SMS} ^{88,86} = -267(45) \,
\mathrm{MHz}$ and $\delta \nu_\text{FS} ^{88,86} = 2(42) \, \mathrm{MHz}$.
Finally, we measure the hyperfine splitting of the ${\mathrm{5s8p}
^1\mathrm{P}_1}$ state in fermionic strontium, and deduce the magnetic dipole
and electric quadrupole coupling coefficients $A = -4(5) \, \mathrm{MHz}$ and
$B = 5(35) \, \mathrm{MHz}$. Our experimental demonstration shows that this
simple and very fast scheme could improve the laser cooling and imaging
performance of cold strontium atom devices, such as quantum computers based on
strontium atoms in arrays of optical tweezers.
