Strobing caused by lights and sallies With the greatest respect to most electricians that do valuable work in churches, most, if not all are not lighting designers and not skilled in the selection of light fittings, just like the ringers and the clients (PCC). Whilst electricians have the experience of putting light fittings in, they are rarely the ones that look at or use them so generally do as instructed on the back of their purchase order from the PCC.
The cause of flicker is generally the lighting rectifier circuit within the driver behind the LEDs and its ability to smooth out the ripple on the rectified AC mains voltage to generate DC. Whilst LEDs are common in everyday life nowadays, the ones without flicker are more likely to be the professional products that come with a much better LED driver at a much higher capital cost. One of the big advantages of professional fittings is that they have a lot more literature about them and can provide flicker-free assurances or a quantifiable amount of ripple. The cheaper LEDs won't have been tested, and are likely to have a ripple many times worse than the ones that have been tested.
I have come across a couple of ringing chambers at towers that have not long been re-hung, where the lighting level is akin to "restaurant mood lighting" at best. There seems to be an underestimation of the amount of lighting required.
From a technical perspective, as it is the driver at fault in these LEDs causing the flicker, it is entirely practicable if the LED fittings allow their internal one to be bypassed, to fit a much better driver upstream, or local to the LED fitting. Some of the professionals LED drivers will output 230, or even up to 300VDC, which would mean you could drive the fitted (mains powered) LEDs direct from another driver without any work to them, and the rectifier circuit within will never see an oscillating AC supply. I have not looked into the cost of this, but I suspect the professional quality LED drivers could be greater than the cost of some of these LED light fittings that are suffering from flicker.