If it is that important to you, Scanner Masters website says they can do the upgrades. Hopefully someone on here has the firmware they'll share with you. Do you really expect a firmware update will improve the life/reception of scanners as old as the PSR-300 and 400? Just asking.
How to update your police scanner firmware. Better understand what rebanding and firmware are, and how to update it on your police scanner at home.
www.scannermaster.com
Improve? No. In fact I'm not even sure what was included in each update as that information can't be found now either. I personally just like to keep things up to date as much as possible.
Rebanding was a thing back in it's day too, and my state police are still on the same 800mhz analog trunk for the time being (being phased out over the next few years for digital) and I still have a ton of analog in my area. I find that I use my 346xt more than my RS197/436HP in fact.
I did see that Scannermaster will do it for a price, but considering I paid $35 for one of the 400s recently I ain't paying more for firmware revisions. According to a PDF chart on their website version 1.7 is the latest for both, and you need 1.5 or higher for rebanding.
I still need to check the other 2 and see what versions they have. I have a feeling the other 400 that I've owned for ages was kept up long enough to have the latest version. Shame I can't find a way to clone it over to the others, only programming. If I can't find it, it isn't the end of the world, but it would be nice to know it has all of the updates GRE ever gave it.