What is the crowd's opinion of UFS Explorer Standard Recovery?

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Download a copy of UFS Explorer. Depending on your setup, you should be able to either see, or select the LUN via the 'open' tab at the top. Scan the volume for lost data. DO NOT save and data back to the LUN.

https://www.ufsexplorer.com/ufs-explorer-standard-recovery.php

Sure, the biggest problem for data recovery in most cases is extensive use of the drive which causes data overwriting, rather than the other way around. Try UFS Explorer (https://www.ufsexplorer.com/ufs-explorer-standard-recovery.php), it supports HFS+, so you can see what can be recovered.

As far as I understand, you don't have to send your external hard disk drive anywhere, you can restore the all the deleted files related to your mailing client (mind that these are usually not just .dat files, but some other files containing service information) yourself using data recovery software. Connect this drive to another computer, scan it with UFS Explorer (https://www.ufsexplorer.com/ufs-explorer-standard-recovery.php) and save the recovered data to another storage. The trial version may suffice to rescue the files you need as they are usually small in size. After that, copy them to the "problem" external disk and configure your email app to use them. However, consider that this will only work if you didn't overwrite any information by using the drive after deletion.

Try scanning your laptop's drive with UFS Explorer (https://www.ufsexplorer.com/ufs-explorer-standard-recovery.php). Use a trial version to see whether the data is available. If it doesn't find anything, chances are that the files haven't been transferred at all due to some glitch or connection issues. Also, they may have been overwritten if you continued using that very drive.