This work has been supported by: Royal Society University Research Fellowship UF160547 ("Black hole dynamics beyond general relativity''); Royal Society Research Grant RGF\R1\180073 ("Numerical Relativity beyond General Relativity''); NSF Grant No. OAC-2004879; NSF Grant No. PHY-2110416; FCT Portugal through grant IF/00729/2015; Computer resources at SuperMUC_NG and the Leibniz Supercomputing Center via PRACE Grant No. 2018194669 ("FunPhysGW: Fundamental Physics in the era of gravitational waves"); Computer resources at Marenostrum IV provided by the Barcelona Supercomputing Center via the PRACE grant Tier-0 PPFPWG; ACTP186 ("Extreme Gravity and Gravitational Waves") -- the DiRAC component of the Cambridge Service for Data Driven Discovery (CSD3) was funded by BEIS capital funding via STFC capital grants ST/P002307/1 and ST/R002452/1 and STFC operations grant ST/R00689X/1.

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