Paid freight bill ??
Just to note, there is jurisprudence in Canada for not having to pay a freight bill prior to instituting a claim for damages.
In the case of: Lentia Manufacturing Ltd. v. Inter-city Truck Lines (Canada) Ltd., 1990
If you want to read the whole thing, here's the link.
Lentia Manufacturing Ltd. v. Inter-city Truck Lines (Canada) Ltd., 1990
A partial quote from that decision follows:
Counsel before us pointed to the wording in Clause 12b and argued that at the commencement of the action which is the subject of the appeal, the respondent owed $7,557.04 in freight charges to the appellant for costs incurred in transporting the goods from British Columbia to Ontario and return, and that the respondent, by not paying the respondent's freight charges, had not met either the required statutory precondition, or a contractual precondition, under the bill of lading. The wording of Article 12a and 12b of the Motor Carrier Regulations was incorporated in the bill of lading. Counsel submitted that the respondent was not entitled to bring the action for damages without first paying the freight bill.
I am unable to accept that submission. In the first place the wording of Article 12a and 12b and the wording of the bill of lading does not clearly state that it is a condition precedent to the bringing of an action for damage, which is claimed to be the responsibility of the carrier, that the freight bill be paid. As I mentioned during the hearing of the appeal I would have expected much more precise language to be used before an obligation was imposed on the respondent to pay the freight charges as a condition to it bringing the action for damages. Further, it would be illogical to require the respondent to pay the freight charges as a precondition to commencing its action when its action is for damages to the goods in question. These freight charges would then became an expense incurred in connection with that damage claim. It is illogical to require the respondent to pay this expense as a condition to its right to recover that expense and other damages from the appellant.
End of quote.
I'm not sure how much you value your relationship with the carrier, but their seemingly lack of care about retaining you as a customer would indicate future behavior. Personally, I wouldn't pay the bill until a legitimate claim against the carriers insurance was acknowledged by the insurer, or they made good your loss. As far as settling with the shipper, your were acting in good faith to mitigate the loss.