Disclaimer: these are just opinions, I do not necessarily have authoritative knowledge in this topic.
If you consider the traditional Sharpe definition:
$$S = \frac{reward}{risk}$$
where reward is the expected return (above risk free rate) and risk is the standard deviation of reward, it is not clear to me how your augmented Sharpe ratio is related to this. Instead, my instinctive approach would be to model the return of the bond under a benoulli distribution with $p_i$ the probability of default, i.e. when random variable $X_i=1$ and no default if $X_i=0$. Furthermore we need some consistency of time so I will measure over a time period $\Delta t$.
$$ reward_i = (100 + r_i) (1 - X_i) + 100(1-L_{gd})X_i - C_i$$
where $r_i$ is the return of the bond over $\Delta t$, $C_i$ is some standardisation, like subtracting risk free rate, and we have a loss given default factor. If you let $R_i=100+r_i$ and $L_i=100(1-L_{gd})$ then;
$$ E[reward_i] = R_i(1-p_i)+L_ip_i-C_i$$
and
$$ Var(reward_i) = Var((-R_i+L_i)X_i)=(R_i-L_i)^2p_i(1-p_i)$$
So you end up with a formula which states that;
$$Sharpe(p_i; R_i, L_i, C_i) = \frac{R_i(1-p_i)+L_ip_i - C_i}{\pm(R_i-L_i)\sqrt{p_i(1-p_i)}} \;.$$
As a completely separate point I would suspect that your machine learning process would benefit by conditioning itself on the data of the timing of defaults. This was a failure of models based on copulas in the credit crisis if I recall. It might end up being quite a complicated formulation of a model that accounts for similarity based on timeliness of defaults.
Happy for harsh criticism.. don't hold back..
