I think you have a two part problem, one part which is fairly easy to fix and the other that could be detailed.
You stated that you had cleaned the line with a chemical drain opener. While it is true that chemical drain openers can restore a passage through a clog, there is no assurance that it actually removed the majority of the clog. The only effective way to insure a drain line is open is to use a powered drain auger fitted with a cutting attachment mated to the size of the line.
You stated that this house is 38 years old, therefore we can assume the laundry standpipe is an 1-1/2" line which was code standard at the time the house was built, however in the mid 1980's the appliance industry changed to a higher volume pump in order to reduce operating time and save energy. The result is that laundry standpipes must now be 2" pipe. You may continue to use the 1-1/2" pipes but do so with the understanding that even a slight buildup of soap residue or a partial clog will render the pipe insufficient to meet the needs of the higher capacity pumps.