I don't think there is a way to test by serial number, but I would assume the higher the number the more likely it has the newer circuits. Users also could have possibly sent their cameras in for repair and could have had their boards replaced.
The viewfinder lcd information brightness is dependent on the light source the camera is pointed at. There is an opaque bar in the front where the pentaprism is. Like I mentioned in my previous post, there is a manual LCD light thats activated on the right side for use in dark environments. Sometimes this can be broken and not light up. Interestingly you mention the F3 as that same light is one of the most commonly broken things on that tough body.
On keh there is a champagne om4t for $200 in bgn condition. For $300 there has been a number of completed auctions on eBay for om3 models at that price range. Unless its pristine in box I think the price is a bit high. Maybe worth it if it's been cla'ed by someone that specializes in Olympus cameras, as the quality of cla's can vary.