My last bike was a softail - and the best way I can describe to take sharper turns is to plan ahead. You have to work your way through the turn (vs. carving through them), and sometimes your just going to scrape. The bike is naturally low, so your speed and lean angle will have to be adjusted for the curve to ensure you don't scrape.
Just don't panic on the scrape, and try to adjust your lean angle if safety doesn't come into play. I have pushed up the floorboards on my softail before, but it was what the conditions called for. I am not encouraging scraping by any means, it just can happen.
On my Street Glide I can pop through corners much faster, and more stable than on my softail. Now that I have gotten comfortable on my new ride, I have scraped the floorboards on my new ride. Kinda surprised me that I could because I feel much higher off the ground than I am compared to the softail.
Lifting the bike is an option, but make sure you can still place both feet flat on the ground after your lift. Shorter floorboards would be lest costly, just make sure you pay attention to where your boot heal is, or you may melt it a bit.
I miss the softail suspension, and I wouldn't compromise your overal ride experience by stiffening up the shocks.