Thanks everyone! This issue has now been sorted out (at least regarding bitni.com).
While the admin of bitni.com was rather slow to react, he did help me and eventually provided me with the proof of payment. Turned out that the party who was supposed to receive this payment (
https://shitcoins.club/ ) had an issue in their payment receiving software and did not credit the payment to me. While they had actually received the funds they refused to help me unless I provide them with a link to the block explorer showing that my transaction has been confirmed. Thanks to the proof of payment I received from the admin of bitni.com I am now able to give shitcoins.club the link to the block explorer as demanded.
So, what we learned from all this... Bitni.com provides a rather mediocre service, which by itself fails to provide the user with the critical information such as a proof of payment. In case of problems there is not much the customer can do other than to contact the slow-reacting administrator of the service. As for shitcoins.club, they should have been able to verify my payment on their own, knowing the payment amount, approximate date and the receiving address. They chose to demand the payment proof from me instead, which was highly complicated due to the fact that the payment originated from an exchange and BEAM tokens have privacy features that make solely address based queries impossible for third parties. Whether shitcoins.club is hoping to keep the money for themselves in case I fail to provide them with the proof or whether they are just lazy and incompetent is currently unknown as I am still waiting for the funds to be credited.
