Are you worried about bumping your head getting in and out, or while driving? My Focus has a high roof line, and I'm strapped in with a 5 point harness, even on the street, specifically *because* of the cage, so there's no chance of bumping it while driving. I don't think you need to worry about getting hurt getting in and out. If the cage is close to your head and the road is bumpy, maybe you could worry about that. I still don't think it would *hurt* much, but you'd feel it. You could try the soft stuff.
In race cars, there's a concern about flammable materials inside, and IIRC, the FIA padding is flame retardant. Probably not worth worrying about with the soft stuff you're putting in.
Another option, if you have money to spend or a REALLY helpful wife, have somebody sew up a padded fabric, velcro closed sleeve to put over top, just like the Jeeps used to have. That would really make it look nice, and give the dual level of protection you want.
One note, the BSCI brand padding I bought didn't work out too well with the self-adhesive strip they put on. I had to zip tie the cage. Others have had the same problem. If you use large black zip ties and trim them, do a neat job, it doesn't look bad at all.