On this shot, with a crop factor of 4.5X on a different camera (Kodak P880) and 25mm actual focal length, you're at 117mm equiv focal length so 1/60th shutter speed wouldn't be adequate for hand holding. The old 'rule' is shutter speed should be at least your 1/focal length but today with the ever increasing resolution of sensors, you might want to aim for double that. Note this is just a general rule and factors like technique and individual ability will influence this.
You can see that the day was more overcast (less light) and your position has changed.

The thing with 60fps at 1MP is that even 1080P video gives you over 2MP resolution. Of course there are other video limitations but there are probably better ways to capture that cannon burst.

In regards to your camera's lag. Is it the shutter lag or AF lag? Shutter lag is typically very low if you're already pre-focused.
Which leaves only the reaction time. So I guess it comes down to how the firing sequence is conducted and how easy it is to anticipate.

With your current Nikon P520, this is what I would try.
Set your exposure manually when it is close to firing. Hopefully shooting conditions don't change rapidly (eg. fast moving clouds where its full sun one second and full shade the next).
Set exposure to under expose maybe 1 or slightly more stops if you're at base ISO.
Check that the shutter speed is adequate. Check your tests shots to see if they are sharp at the focal length of your framing and that the rest of the scene is not too dark (you can boost the shadows a little in post processing).
Set to the max continuos shooting speed at the max resolution, 7fps in your case.
When the conductor starts his sequence, pre-focus with a half press and hold that position.
Then try to time the start of your shooting burst at the start (or just before) the cannon fire.
This way you have less files to sort through and the one you get is of higher quality.

I have to say I don't use continuous shooting much and only do it if I'm trying to capture a sequence. Depending on how many times the cannon fires, I'd be tempted to use just a single frame and time each cannon fire with a single frame each time. I just find I have better success doing it this way for capturing decisive moments, rather than bursts but that's just me.
Stick to continuous shooting if there aren't many cannon fires (ie. you don't get many goes at timing the shutter) or things are less predictable and difficult to time.