From OLS regression to Logistic Model

I'm currently working on my master thesis in finance. Without going into to much details, my goal is to regress certain predictors on first-day returns (SPAC IPO performance). However, after performing multiple regression analysis on my data, it seems like one of my predictors (shares redeemed) drives the results and the others are just proxy for that. That is, shares redeemed is significant on a 1% level, but the others are not.

One possible explanation for this could be the fact that shares are redeemed concurrently with the IPO-merger, whereas the rest of the predictors (balance sheet fundamentals) are already known for the shareholder deciding to redeem or retain their shares.

In order to account for this problem (cofounding?), I have ran a logistic regression using shares redeemed as the dependent variable, and the rest of the predictors above (in the original regression) as predictors in this model too. The summary statistics shows that one of the predictors (total assets raised/IPO proceeds) is significant on a 10% level. Moreover, when trying to perform an in-sample prediction, the model-accuracy is about 67%.

My question is: is this the right way to think about it, or should I use a different approach? I have tried to remove shares redeemed from the multiple regression, and this yield other significant variables. However, much of the thesis revolve around shares redeemed, and I do not want to exclude this from my analysis.