Honestly, I'd probably kludge this one if possible.
See if you can add an optional flag as a parameter to the proc to indicate that the first result set is not to be returned, only the second. Then you can capture the output from the proc directly into a temp table, for example, since it will then be only one result set.
SQL DBA,SQL Server MVP(07, 08, 09) Prosecutor James Blackburn, in closing argument in the Fatal Vision murders trial:
If in the future, you should cry a tear, cry one for them [the murder victims]. If in the future, you should say a prayer, say one for them. And if in the future, you should light a candle, light one for them.