I'm willing to bet your dad is on a Comcast line or some other VOIP line.
In that case, the 500's louder transmitter output (as compared to the 302; this being one of the key aspects of the 500 design, to enable it to be used on longer loops) is probably causing the echo to begin with, and the Comcast or whoever's ATA or possibly central office switch, is using echo canceling, which takes a little while to kick in on each call.
One possible fix for this is to put some kind of dropping resistor in parallel across the R and B terminals on the 425 network block, to reduce the transmitter output to the same level as the 302. Finding the correct value of resistor would take some doing, to get the volume down to exactly the right level.
One way to do this without a bunch of test equipment, might be to take a variable resistor ("potentiometer") at about 25 K, and solder two leads onto it (center contact and one of the outer contacts), connect them to R and B, and then quickly make a series of brief phone calls to another phone (e.g. your cellphone) whilst setting the potentiometer at various points to see what works best. You'll need to have good enough ears to be able to remember the loudness of the audio from each test, starting with the 302 as a reference point. Then when you find the correct setting, use an ohmmeter to measure it, and go buy a resistor (rated 1/4 watt or higher) at a value that's as close as possible to the one you measured.
Note, the sidetone level on a 500 set in normal use is a tad lower than on a 302, so it's also possible that someone who is used to a 302 will tend to speak a little more loudly on a 500 in order to hear the same amount of sidetone. Speaking more loudly will also produce the result of louder output and greater echo.
Alternately you could just "get used to it" and think of it as one of the "cute" transmission artifacts of "modern" (VOIP) telephony. If you internalize the worldview that real life has become dystopian science fiction, everything makes more sense:-)