Capacitor for LED flickering

I'm a newbie here so please be charitable.

For the last 25 years I've had trouble keeping the clock set on my microwave ovens at my church. Since they are in a low use area it will generally be a week between seeing the clocks and they are always reset to 000 from one week to the next like there has been a power interruption sometime that week. No other real electrical problems noted. Sound systems are on UPS so any power fluctuations are smoothed there. My question now is, the fluorescent lighting has been deteriorating requiring replacement ballast, bulbs, and etc so I decided to install LED tubes. I cut out the ballast and installed straight wired LED tubes -- no problem, they work great! However, they occasionally flicker for a few seconds and I suspect it is due to fluctuations in line supply. I have discussed this with my power supplier who say they have checked everything out and all is nominal from the supply side. (I find that hard to believe with my 25 year history). I believe the problem is intermittent and difficult to diagnose from their perspective. The transformer on the building is probably 50 years old, but they are loathe to replace it on a whim.

Now, my question: -- would a capacitor in the line smooth the supply to each of the LED bulbs allowing them to operate without the occasional millisecond flicker. If so, what capacitance should I install? I've got 16 tubes installed in one room and they all blink at the same instant, so I don't think it's a single tube power circuit problem.