As the current increases so will the voltage requirements. If you have it locked at 2.2V then you won't be able to go any higher with the current. Try setting the voltage to 2.5V and slowly increasing the current from 0V. You may need to go even higher than 2.5V to get the full output but that's...
It depends on the diode but most of the higher power multi-mode diodes have pretty terrible divergence. A beam expander will help quite a bit though depending on exactly how far you're trying to point.
It mostly has to do with new shipping regulations. Lithium batteries aren't allowed to be sold separately in marketplaces like Amazon and Ebay anymore unless they come pre-installed in the equipment.
I think this or a less powerful version might be the pump diode: https://www.ebay.com/itm/254310199749
The module certainly looks like it has a C-Mount diode inside.
I was able to capture some photos through a welding mask and playing around with the camera settings. It lasted for quite a bit longer than I remember other ones lasting for. My eyes don't seem to hurt at all but I'm probably immune from staring at laser beams every day. LOL.