Deriving new continuous variable out of logistic regression coefficients
Deriving a probability value (the continuous variable you are talking about) from the logistic model is a perfectly sound thing to do. The probability value is actually the main output from the model.

Getting from the probability value to a decision rule (e.g. from default probability to credit granting decision) is an another step that will also need to incorporate a number of business decisions concerning risk appetite - i.e. how risky clients are you willing to approve not to miss a potentially large amount of business, what the interest is going to be for different risk scores etc. The tradeoff this refers to is the well known sensitivity-specificity tradeoff which is, apart from the confusion matrix you are using, probably best visualised by the ROC curve.

From the confusion matrix it is also apparent that you were training the model on a balanced sample (default rate around 50%). This is quite unusual in credit risk modeling, usually the default rate is well below that. If that is the case, you will probably need to calibrate the probabilities, for example by fitting a yet another logistic regression model on your probabilities as a single variable (this works best when the probabilities are normally distributed). The calibrated probabilities that this second model will predict will accurately reflect the actual real-world probabilities of default.