I decided to find out.
Below is the raw data; the method I used was to count the bursts (I mashed and reloaded) in an interval of 60 seconds and multiply it by the burst count for a rounds per minute value. The first in each group is me without gunslinger, the second with. I was actually kind of surprised at the results.
Protogun: 90 RPM
Protogun (+): 96 RPM
Alchemer: 64 RPM
Alchemer (+): 70 RPM
Autogun: 240 RPM
Autogun (+): 240 RPM*
*There was a small difference. The first ended at the finish of the previous burst. The second was at the very beginning of the next burst, so you did gain some time, albeit minuscule.
Conclusion: Make the Gunslinger armor line better. There is currently no reason to wear it considering how much more useful swords are anyway. Feel free to retest my results for error.
I think your results are spot on. I feel like Gunslinger's bonus is effective in proportion to the clip size of the weapon. With Blackhawk, I do notice shots going off in greater rapidity, but reloads don't seem to get the same speed benefit. So guns which fire more before the clip runs out receive closer to the intended bonus -- which is still fairly minuscule.
If you pick up an Antigua, I'd be curious to see you replicate your above test for that weapon given its greater clip capacity. Or maybe I'll give it a try when I get home...
(Similar thread with similar discussion: http://forums.spiralknights.com/en/node/3389)