I know nothing about that ATA (other than it appears that it would have been locked to Vonage at one time) and have never used it, so I'm hesitant to suggest anything.
However, that error message, if it's coming from Freephoneline, usually refers to the User Name in the ATA being wrong. With unlocked ATAs, sometimes they're not truly unlocked and suddenly end up being provisioned by the original service provider after an interval of being online. When the problem occurs, check to ensure your SIP Username, which is found after logging in at
https://www.freephoneline.ca/showSipSettings, is entered for the User Name field in your ATA. Also, for troubleshooting purposes, enter the exact same number in the Caller ID number field. Ensure that User Name and Caller ID Number start with "1" (without the quotation marks).
Note that only one registration per FPL account is allowed at any time. When there are multiple devices/softphones using the same account, only the most recent registration is valid. The previous device will lose registration. This is especially important to consider if someone else is using your SIP credentials (username and password) that are found after logging in at
https://www.freephoneline.ca/showSipSettings or if you're trying to register your FPL account with a smartphone SIP app or with another device. Registration is required for incoming calls. It is not required for outgoing calls. The significant concern, though, is that multiple registration attempts can lead to temporary IP bans. The more devices being used can make the temporary ban happen more quickly. Note that each time you reboot or restart your ATA or SIP app, it's attempting to register with Freephoneline again. Multiple registration attempts within a short period can result in temporary IP ban. Each time you reboot your ATA it's attempting to register with FPL's proxy server.
So, I would unplug your PAP2 while you're testing, and I would use a different proxy server than the one you're using with your PAP2. For example, if you're using voip.freephoneline.ca in your PAP2, you can try voip4.freephoneline.ca:6060 in your D-Link ATA.
When you're logged in at
https://www.freephoneline.ca/showSipSettings, SIP Status needs to show connected, and your SIP User Agent needs to indicate your D-Link ATA and not your PAP2.
I can't find a manual that discusses anything about D-LINK dial plan syntax, which I'm unfamiliar with (I'm not positive what the "T" does), but the first and third digit maps you posted are basically the same. 0xx.T, I'm guessing is for 011 (international calls) followed by any number of digits. If you're dialing the exact same number in all instances, then I doubt the digit map is the issue, but I would not use the second one.
If the number you're dialing has been ported recently, wait a few days to test again. It may be an intermittent issue that resolves after a few business days, if the problem is related to trying to reach a recently ported number.
Otherwise, I would suggest asking at
https://www.dslreports.com/forum/voipSomeone there may have experience with the VTA-CV ATA that I've never heard of before until now.