I used to have a Grant steering wheel long ago on a 69 Mustang HardTop (coupe) I had in high school (early 70s). I was able to solve my horn issues by installing a horn relay. When reading RackerM's comment, above, I found myself nodding in affirmation with his every suggestion/thought. I have some weak sounding horns on our 73 Mach 1 Mustang currently, even with new horns. Since it is not a high priority on my little To Be Done list, I have not tried to measure the amperage at the horns (via inductive ammeter). But now, after reading the posts in this thread, I am inspired and will be returning to that issue.
We also have a 73 Mustang vert that has decent sounding horns. So, I will first measure the amperage draw for both vehicles' horn circuits, where the wiring on both Mustangs is stock, and being pushed through the stock steering wheels with their related contact brush/ring setup, and see if maybe it is the amount of current making it to the horns that is making the the difference in sound quality. If I see no significant difference I will swap horns between the two cars to see if the problem follows the physical horns or not. My gut tells me I am going to end up installing a horn relay in the Mach 1 at the least. When I make an improvement with one of the 73 Mustangs I tend to do the same for the other one whether it is needed or not, just because I like to tinker with them if for no other reason/excuse.