Settings on the TG-5 are not always straight forward, particularly with program type modes such as microscope. The camera has 3 apertures available, f2.0, f2.8 and f8. f 8 is achieved with a ND filter.
Exposure compensation will only work the shutter speed/aperture, flash exposure compensation doesn't do anything as I believe the flash is just there as a trigger to set off a burst of light from the LED - so the camera does not behave as you would expect it would with a flash, because both shutter speed and aperture impact exposure from the LED. The way to get the exposure correct is to decrease shutter speed, but of course you can't access this directly as there is no manual control of aperture/shutter speed. I suspect what is happening is the camera is metering with low/no light then takes an image based on that but the output of the light goes up when triggered by the strobe.
So how is the ring light setup? is it running at 1800 lumens then kicks up to the full 3000 when triggered, or is it no light then full power? 3000 lumens is not quite double 1800 lumens so should be within the range available from exposure compensation - about 2/3 - 1 stop higher output, so in theory setting exposure compensation to -1 should work. But if you were running 1/2 or 1/4 power to save batteries then got full power it would blow out. When I say exposure compensation - this is camera exposure - NOT flash exposure compensation. I would also suggest using Av if you can achieve focus where you need it, it takes one more variable out of the equation.
The TG-5 also has the ability to set flash to manual, if you are only using it for triggering then you might as well do that, set it to minimum output and save a little battery power and get faster recycle.