Looking for an algorithm that correctly clusters visually separable clusters
With appropriate parameters, DBSCAN and single linkage hierarchical agglomerative clustering should work very well. Epsilon=0.2 or so.

But why? You know the data, just use a threshold.

If you just want an algorithm to "confirm" your desired outcome then you are using it wrong. Be honest: if you want your result to be "if $F-factor-1 > 1.5 then cluster1 else cluster2", then just say so, instead of attempting to find a clustering algorithm to fit to your desired solution!