NOT an options expert so ... Example: Long 1 Call has Delta 40. Long 1 Put has Delta 50. Buying 10 shares of the stock will equalize Delta but that will change as price changes and time passes by.
You buy straddles when vola is low. You can then gamma scalp to earn back the lost theta till de vola rises, you can then close the positions with profit, see https://tickertape.tdameritrade.com/trading/scalp-gamma-dynamic-hedge-16089
IMHO, I think O.P. realized he was going down a rabbit hole by attempting to equalize directional exposure, when a straddle was really not proper choice for what he wanted. -- I am guessing, of course.
You can't really eliminate losses on straddles but what you can do is reduce it by making better guesses of what the future volatility is going to be and by selling some options to reduce your cost so in case where the volatility is not as big as you predicted, your loss is mitigated somewhat. There is no way to buy options with strikes at EXACTLY where the market price is unless the market price happens to fall EXACTLY on the strike although some options strike match very very closely to the underlying's market price. Due to the put/call parity if you spend the same amount of $$ to buy calls and puts you will always end up with more calls than puts or vice versa. What I do is I buy the same quantity of calls and puts and if I happen to spend more $$ on calls or puts, so be it. Hope this helps.