Hi Thomas and Kyle,
If the data was collected with GPScorrect on the handheld, then I think the only way to post-process would be to temporarily go back to GPS Analyst or you could process the data in Pathfinder Office. If you don't have a license for Pathfinder Office, you may be able to get a 2-week evaluation copy or send the files off to your local reseller, and they may be able to process for you.
If the data was collected with Positions extension for ArcPad, then you should be able to use the Import QuickProject functionality in Positions Desktop Add-in. This might also work with GPScorrect.ssf files, I just haven't tried it. If interested, let me know, and I can put some more detailed directions out here.