In practical terms to recover original target in REDIRECT you have to use the obscure SO_ORIGINAL_DST, while for TPROXY getpeername() will just work.
By this token TPROXY is a bit easier to use. This is for TCP. UDP is a bit harder.
perhaps this works poorly for firewalls near to the service but you declared the problem to be one close to the client. AIUI
But you don't know who dropped it: the ISP or the remote server. In order to show it's the network between the client and server dropping it, you need a server that behaves in a known way, hence open.zorinaq.com I used to work in the InfoSec industry, running port scans from various locations, and open.zorinaq.com was incredibly useful to ensure there was no random firewall preventing us from finding certain open ports. That was the primary motivation why I built the service.
http://open.zorinaq.com/
The folks at Cloudflare have done it with an iptables TPROXY rule (which requires the socket to have the IP_TRANSPARENT option) which is how I did it too. But there is another way to do this in Linux: you can use an iptables REDIRECT rule, and the userspace program can obtain the original destination port by doing a getsockopt() call to read SO_ORIGINAL_DST.
Edit: oh I see now the blog post does mention the REDIRECT & SO_ORIGINAL_DST option, but criticize its performance... which makes sense given its dependence on conntrack.
There is a typo in Cloudflare's blog post: s/SO_TRANSPARENT/IP_TRANSPARENT/