you need to make some pretty strong assumptions to overcome a 1:170,000,000,000 difference.

Actually you don't. Consider the following highly simplified toy model.

You're not sure where the great filter is but you think there is a 50% chance it's before evolving intelligence (scenario A), and 50% that it's afterward (scenario B).

In scenario A each galaxy only has a 0.1% chance of having intelligent life. (Note that nevertheless the observable universe will still have life somewhere since 0.1% is a lot more than 1/170,000,000,000.)

In scenario B each galaxy has (multiple) planets with intelligent life in it.

Combining these two scenarios gives 100% for life in the universe and 50.1% for life in the galaxy.

By changing these numbers and adding more scenarios you can get different but similar results. You should try this yourself, it's a good way to get an intuition for how Bayesian probabilities work. For example, try adding a scenario C where intelligent life is extremely rare and we exist only due to the anthropic principal. What happens when you assign scenario C 40% and keep scenarios A and B equally likely?