It is not overwhelmed at all.
You have to understand that the price shown on coingecko/coinmarketcap is not the "real" price, because they are ignoring the highest volume price source: the internal market.
If they correctly accounted for this, you would see that the peg is holding much tighter than they are currently reporting.
Instead they are incorrectly reporting the price on upbit, because by discounting the trading on the internal exchange, it appears to them to be the largest volume of trading. But upbitrestricts who can trade there (I think it's for Koreans only), so it is only to be expected that the price on upbit can stray from the overall market price. And if you can trade on both upbit and the internal market, you can make some small profits that way.
RE: Data On HBDStabilizer | HBD bought, sold and profitability