If you alter the location of your toss, both left to right and how far into the court vs above you it goes, that's going to alter the angle and movement or the racquet at the exact moment of impact. Sounds like your toss goes a bit to your right and out into the court. Toss the ball less to the right. Sounds like you feel like your serve is too much spin (I'm not sure, exactly, from the description) and not enough pace, in which case you probably need to have your toss be a little more out ahead of you, instead of straight up or even behind.
If you want heavier topspin, a bit more of a backhand grip vs. an open grip will also impart spin vs. a flatter serve, though a neutral, "continental" grip is pretty reliable for all types of serves, and if you learn to hit different types of servers with the same grip, the grip won't tip your opponent to what is coming.
Here is a YouTube video that shows the differences between a slice (sounds like what you have) vs a kick (heavy topsping) vs flat serve -
Tennis Serve In Slow Motion - Kick Serve/Slice Serve/Flat Serve
and a how-to with animated GIFs
Tennis Companion: 3 Types of Tennis Serves