Should I be trying to change my stroke to hit more topspin, or continue to go with hitting flat as my first reaction?
It depends upon what sort of problems are involved here.
Do you have troubles sustaining a rally? Most rallies end with an unforced error, but they also typically end within very few shots. So, you do not always need incredible strokes and you don't need to be able to hit an average of 20 solid balls in a row. Most of them need to be just enough to keep your opponent cool and you need to hit an average of maybe 5 like that. If you can do that, consistency is not your problem.
A different problem would be that you simply cannot hit a good top spin shot. I am not talking about your average rally ball which, despite its more direct trajectory, still does have some top spin on it. I talk about something that arcs high above the net, digs down fast and kicks high (hopefully, above the shoulders of your opponent). If you can't produce that ball, it's a problem. If you send the ball higher and expel more energy to generate top spin beyond your average stroke, it is very obvious that this ball can't go as fast as your typical ball does. So, it's a ball that can buy you some time. Furthermore, very few amateur are geared to attack high balls which also makes it one more thing you can use to annoy your opponent.
So, what should you do? If you are consistent and can bring yourself to hit the sort of ball I talk about on occasions, you don't need major changes. You could want them, but, in themselves, they would not make you a better player.
Is there any way to improve the heaviness on my ball without changing my mechanics in a big way?
The sensation of heft result of a combination of spin and pace. That is, an heavy ball is what comes out of a powerful motion. There are small things you could do, as well as bigger ones, to improve in this area. However, it's hard to say what you should do without seeing you hit a forehand.
Typical small adjustments include what you do with your shoulders, your non-hitting arm or the position of your feet; typical major adjustments include things like learning a new stance or dramatically changing your swing path.