I was using genesis mining before but i stop using them because i bought my own miner and genesis mining is less profit and much possible to be happen they can be scam in the end.. Anyway i think you can use your binance bitcoin address as long as you maintain the bitcoin address..
Why not use the segwit address instead? if you are having slow transaction and high fee it can fix your issue by using electrum wallet latest version and use the segwit addresses it can reduce your size of the transaction and pay less fee than a legacy wallet...