You don't really need anything else.
If you look at books like "Practices for Scaling Lean & Agile Development" ( http://amzn.to/18gfbWJ
) the common theme is that the piece you need to embed Scrum and the lean-agile practices you are looking for is not going to come from more rigour heaped on top of the scrum framework.
If you are not getting lean-agile principals embedded at a high level that would indicate a lack of desire for adoption and change at that level. This is normal and there is no formula to engender those ideals. One can use SAFe to give the organisation the same... mechanics that teams sometimes achieve with Scrum, but mechanics are not principals.
There is no formula, but creating Communities of Practice and introducing your executives to workshops in lean-agile principals can help 'flip the light-bulb' on for many... others will never get it...
It may be that the best you can do for now is SAFe to get everyone going in the same direction. You do however need to watch out for the illusion is a successful adoption that it can often create.