Do you get any benefit from the other columns? Suppose you remove the textdata column from the output. What are you left with, then? You may still be able to filter based on part of the textdata, but I have not tried this, before. It may also be possible to just dump the trace to a file directly, in case the Profiler application is getting stuck with a small textsize parameter. Script out the trace, and run that as a job to see if this gets you anywhere (on a test server, of course).
Also, does the BizTalk integration need to set the textsize for the connection? 70 MB is just outside the default value.
Of course, if you have access to the stored procedure itself, you could toss in some insert statements and direct some output to a log table.