clustering - Performance issues with (clustered) point features

How do I get a point features layer containing roughly 2800 labeled features to perform smoothly when exported (and converted to GeoJSON) with qgis2web?

Specifics: I use qgis2web 3.4.0 and QGIS 3.2.3 to create web maps and am experiencing performance issues with the following map.

http://www.rv-k.de/LK_Esslingen/Fahrradwegweisung/Abstimmung/Online.html

Things I have tried:

1. 
   

   File size
   Overall file sizes are not very large. Still, I tried to further reduce file size by changing export precision settings. No performance gains.

   
   
   


2. 
   

   Number of features per layer
   The layer "Knoten" contains roughly 2800 point features and seems to cause the performance issues because broken up into 5 different layers (with 700 features per layer max) and turning off labels for each layer, the map performs fine. (Other layers contain significantly less features.)

   
   

http://www.rv-k.de/LK_Esslingen/Fahrradwegweisung/TestGIS/5Layerstest/5LayersGIS.html

3. Clustering features
   Still, I need all features to display as one layer and with labels. Therefore, I tried clustering using https://github.com/Leaflet/Leaflet.markercluster. There are still performance issues because all 2800 features are loaded at the same time once you go beyond zoom level 16. Still, I need the markers to display individually at this point and therefore set (disableClusteringAtZoom: 16).

http://www.rv-k.de/LK_Esslingen/Fahrradwegweisung/TestGIS/Clustertest/WebGIS.html