I think I would have done the repairs from the backside, used a thinner paper-based material (something that could, when used with a thinned water-based glue, be formed to the ribbed shape of the cones...like a very thin paper mache), and kept the patches as small as possible.
EDIT - if the tears are small, with thin gaps, another alternative is to use stretchable fabric glue with no patch, applying several coats.
And if the cones are tearing because of age-based degradation, you might think about coating them with a thin slurry made from white glue and distilled water, brushed on (assuming they are paper cones). This will strengthen them, with minimal added mass.
The same "slurry" would be used to apply paper patches. It helps meld the patch with the cone.