For preserving privacy, blockchains can be equipped with dedicated mechanisms to anonymize participants. However, these mechanism often take only the abstraction layer of blockchains into account whereas observations of the underlying network traffic can reveal the originator of a transaction request. Previous solutions either provide topological privacy that can be broken by attackers controlling a large number of nodes, or offer strong and cryptographic privacy but are inefficient up to practical unusability. Further, there is no flexible way to trade privacy against efficiency to adjust to practical needs. We propose a novel approach that combines existing mechanisms to have quantifiable and adjustable cryptographic privacy which is further improved by augmented statistical measures that prevent frequent attacks with lower resources. This approach achieves flexibility for privacy and efficency requirements of different blockchain use cases.