These rebroadcasting services can only rebroadcast a transaction from its transaction ID if they have the transaction in their mempool already.
This is obvious.
From searching for his second transaction, I cannot find it in any mempool.
I thought that you talk about fe682ab28ecdb3bc82498af0c7730e2fcb0cf8563c6fc88cc2367c16aa3624a0
I've checked more and I guess that you were talking about b405185bc699d24a611cb25aeb3347159235c968bbb0d58a8c98cc1b96cd6ccf which indeed is rara avis.
But I can always rely on chain.so to find such transactions and again it doesn't disappoint
Is the hex tx from here enough for re-broadcasting it?
Edit: I've re-broadcasted it, the hex tx worked with coinb.in