Spin is an illusion man, it's like There but it's not something that's easy to get more of man. It used to be one of the first things I thought about now it's the last thing I care about.
You've hit your awkward range: good grip, smooth flat and straight will be your friends more than the fickle spin. That being said the best way is to load your body/arm/hand more. Try grabbing the disc further around the side for more spin, use a rocking motion towards the basket.
Rock forward, back, forward. The backswing actually helps get more snap on it, load the disc on rock back. When you rock forward.. Push off with your back leg, arm loaded, just before you get the weight on your front foot the arm should be moving, when the weight hits your front foot coordinate it so you snap/throw the disc at a split second after.
If I'm a ways out I cock my body on more of a 45 degree angle so I can get a further reachback but as soon as I try to add spin for distance I miss left (LHBH) because I torque my shot. Try to remember what works at 30ft, keep doing that. Better.