"Is it possible the line crossed the river twice, once at Clarksville and once at Van Buren?"

Yes. it is quite possible that branch lines would have crossed the Arkansas River at both Clarksville and Van Buren. Again whatever would have been the shortest possible route to string the wire and use the least amount of wire possible.

Another possible answer is that the telegraph line crossed the Arkansas River at Van Buren and then ran the North side of the River to Clarksville before crossing back to the south side at some point between Clarksville and Little Rock. This would also explain why the Clarksville station would have been involved in passing those messages. That is actually the most plausible explaination to me without other evidence. And even simpler answer is that the telegraph operator simply had a messager take the ferry across the river to the station on the other side rather than run telegraph line under the Arkansas River.

Again terrain features would have contributed heavily to these decisions. That is why most telegraph line ran along established roads not only for ease of maintance, but more so because established roads usually followed the easiest terrain features and crossed rivers at the most serviceable fords and ferrys.