An update regarding this. I filed a USDOT complaint on March 4. Received a reply from the USDOT on March 23 saying they will forward the complaint to TAP. TAP replied to the forwarded email on April 13 saying that a refund had been initiated. Received a refund in full back on my credit card on April 19.
So I highly doubt TAP was actually intending on refunding me until USDOT was involved. I did file a dispute with my credit card company in late March but I haven’t received any correspondence from them yet.
Lesson learned. TAP’s 24 hour cancelation policy is bunk.