How to properly ground new three way switches being installed?
The proper way is indeed to pigtail ground wires from that bundle to each switch. They should be wired in such a way that detaching ground from one switch (to replace it, for example) doesn't impact the grounding of the other switch or anything down the line.
If this makes your bundle of grounds large, you may need to upgrade to a larger wire nut. The wire nut container should have a list of color-coded sizes and the number and gauge of wires it supports.
Side note regarding wire nuts: they should hold every wire very very firmly. Many pro electricians around here note that amateurs don't connect the wire nuts firmly enough and encourage a &quot;yank test&quot;: after connecting the wire nut, yank each wire pretty hard. If it comes out, the wire nut isn't connected firmly enough or may be the wrong size.