That's a tough one. If you really have 3/8" of end play that sounds like an awful lot. Check to make sure everything is installed correctly.
Mine was pretty loose end to end AND it made an odd rattling sound at idle, so I replaced it. As I said, the new one didn't seem much different, but I figure that once everything is installed, the pump arm tends to make it run where it should.
Now, the new one from Ame's Performance was something like $40, so if it's peace of mind you're after, I'd say replace it. You may not notice much difference in end play, but you'll know it's new and that it's right. Plus if you try to use the old one and you end up with a problem, it's a pain in the ass to go back after it. The downside now is that you're ready to go back together and you'll have to wait for your part unless it's available locally (which it probably is and maybe cheaper).
If you can get it locally, get it from Napa or some other reputable retailer, not Autozone, O'Reilley's, etc.
When the only tool in your toolbox is a hammer, you tend to see every problem as a nail.