It was discovered that the HTTP publisher was sending all the point values, but it was putting multiple values into single GETs or POSTs, which the receiving end was not able to handle. Resolution was found by introducing an intercepting layer to send them on to the other program one at a time, as there is not a setting on the HTTP publisher to limit values per message (it's limited by URL length, post size, etc).
Another option that was presented was using the point links to set the HTTP desired directly out a TCP/IP data point rather than tying the point links to a virtual point and having the HTTP publisher do the transport. This likely would have worked, but the existing solution was touched up before this was attempted.