Supports changes within a model

[kmanstudios 1,120]

I had to start a print several times trying to get a part to support properly. The problem was that to get the support to work properly on this tiny part was to put my overhang at 35°. This caused massive amounts of support everywhere else. If I set the supports to the model needs as a whole, this is what I got:

As you can see, the little funnel shape did not get support around the edges and would just knock off and print goo around the space.

To fix this, I kluged up this solution: I split the model into two parts and used the individual settings to use the small area with 35° overhang and the other part at a regular overhang angle. Worked like a charm as you can see in this image:

It works, but I am wondering if there is a better way. I have tried following a thread with a description about 'anti-overhangs', but am confused as to how to actually apply it here as well as would really prefer some sort of visual guide.

Basically, is there a more efficient way to do this properly? Tweak at Z was a thought, but it would not give me an actual preview of the results as it is a post processing setting.