GeoTIFFS on Geoserver are served slowly, at too low resolution

I have a bunch of large, high resolution GeoTIFFs, that I am serving using GeoServer. I also have a prototype client I wrote using Leaflet. The resolution of the TIFFs is quite high, but despite that I get unpleasant, low resolution imagery on my client and also on the layer previews using the GeoServer interface.

The GeoTIFFs are stored as an Image Mosaic; I then created a Layer from it and then seeded the tiles using the GeoWebCache interface.

In my Javascript client I use this code to add the layer to my map:

app.currentTileLayer = L.tileLayer.wms('http://mygeoserver:8080/geoserver/wms', {
            layers: 'myworkspace:layer-name',
            format: 'image/png',
            version: '1.1.1',
            transparent: true,
            tiled: true,
            attribution: '© Myself',
        });

I get the layer all right, but, as mentioned above, it is very low resolution - pixelated is the word I'd use. Also, despite the tile caching, it takes such a very long time to actually get the tiles.

Obviously I must have set some options incorrectly. What could I check?