I am not sure net clearance is a strong indicator of whether its a top spin or flat shot, pros can hit a very hard shot which just clears the net and with a ton of top so it still lands deep.
But if its landing around the service line, then I think you want to get it deeper. So either hit it harder with same net clearance, or hit it as hard with more net clearance, and as you hit it higher over the net, you will see that you will need more top to keep it in.
And changing grip? I would hate anyone to give me that advice before I tried some of the above - especially if I liked my grip, was comfortable with it, and discovered a bit of tweaking my shot let me still use that grip and get the results I wanted.