In general (i.e., for nonzero prior means), the posterior mean in the normal-normal location model is $$ \frac{1/\tau^2}{1/\tau^2+n/\sigma^2}\mu_0+\frac{n/\sigma^2}{1/\tau^2+n/\sigma^2}\bar{x} $$ for a prior mean $\mu_0$, a prior variance $\tau^2$ (so notation is slightly different from yours, see https://www2.bcs.rochester.edu/sites/jacobslab/cheat_sheet/bayes_Normal_Normal.pdf.

Hence, the posterior mean is a weighted average of sample mean and prior mean. So if you want to the posterior mean be be further away from zero than the sample mean, you would need to pick $\mu_0>\bar x$ if $\bar x>0$ and $\mu_0<\bar x$ if $\bar x<0$.

But, since you should pick your prior before seeing the data, it is not clear how you would achieve that in general.

In general (i.e., for nonzero prior means), the posterior mean in the normal-normal location model is $$ \frac{1/\tau^2}{1/\tau^2+n/\sigma^2}\mu_0+\frac{n/\sigma^2}{1/\tau^2+n/\sigma^2}\bar{x} $$ for a prior mean $\mu_0$, a prior variance $\tau^2$, a population variance (assumed known here) $\sigma^2$ and a sample size $n$ (so notation is slightly different from yours, see https://www2.bcs.rochester.edu/sites/jacobslab/cheat_sheet/bayes_Normal_Normal.pdf.

Hence, the posterior mean is a weighted average of sample mean and prior mean. So if you want to the posterior mean be be further away from zero than the sample mean, you would need to pick $\mu_0>\bar x$ if $\bar x>0$ and $\mu_0<\bar x$ if $\bar x<0$.

But, since you should pick your prior before seeing the data, it is not clear how you would achieve that in general.