EURECA architectures have been proposed as an enhancement to existing FPGAs, to enable cycle-by-cycle reconfiguration. Applications with irregular data accesses, which previously cannot be efficiently supported in hardware, can be efficiently mapped into EURECA architectures. One major challenge to apply the EURECA architectures to practical applications is the intensive design efforts required to analyse and optimise cycle-reconfigurable operations, in order to obtain accurate and high-performance results while underlying circuits reconfigure cycle by cycle. This work proposes novel compiler support for EURECA-based designs. The compiler adopts (a) techniques based on session types to automatically derive a runtime reconfiguration scheduler that guarantees design correctness, and (b) a streaming circuit model to ensure high-performance circuits. Three benchmark applications -large-scale sorting, Memcached, and Sparse Matrix Vector Multiplication (SpMV)- developed with the proposed compiler support show up to 11.2 times (21.8 times when architecture scales) reduction in area-delay product when compared with conventional architectures, and achieve up to 39% improvements compared with manually optimised EURECA designs.