PAWTUCKET, R.I.—For the first time in more than a month, Chris Schwinden could finally unpack his suitcase.

In the span of 35 days, he belonged to four organizations, played in three leagues and traveled a total of nearly 6,000 miles. So after the longest road trip of his life—one that started in New York and then somehow circled back to Buffalo five weeks later—Schwinden just wanted to go home.

One...