Usually the tippers underreport because of splash out from the tipping mechanism. This is mostly during heavy rates with rapid tips. Of course the tipper can be calibrated by turning the set screws. Unscrewing them raises them creating more frequent tips. Screwing them in is obviously the opposite.
The Stratus is only a 4” diameter opening as well. The standard NWS gauge is pricey, but is 8” diameter. All of these gauges are susceptible to errors due to wind turbulence over the gauge although the newer Davis hourglass design minimizes that.
An option for the Davis crowd is to replace the Davis gauge with a Rainwise 8” electronic gauge. I’d have to look up how, but I know there is one that’s compatible.
Novalynx has a couple of manual 8” gauges...
https://www.scaledinstruments.com/shop/nova-lynx/rain-gauges-2/nova-lynx-260-2510-standard-rain-and-snow-gauge/
https://novalynx.com/store/pc/260-2520-Forestry-Rain-Gauge-8p237.htm