As we mentioned on the previous post, we couldn't see a problem with API throughput when we brought your blockchain up on a regular low-end server. So the most likely explanation is that something is hitting the API hard with requests that take a long time to respond to.
To help identify if this is the case, please stop MultiChain then run it as usual with the parameter -debug=mcapi added to the command line. That will add mcapi lines to debug.log to show the API requests received and when they are completed. If you post all the matching lines from a one minute period here, we can take a look.