When you take 300 mA and the voltake over the LM317 is 24 - 8 = 16 volt. The power into the LM317 is 16 x 0,3 = 4.8 watt.
So you have to cool that power down. The power in the LM7805 is less 0,3 x 3 = 0.9 watt. For this power you need also cooling.
LM2578 is may be usable