Modern mobile communication receivers are often implemented with a direct-conversion architecture, which features a number of advantages over competing designs. A notable limitation of direct-conversion architectures, however, is their sensitivity to amplitude and phase mismatches between the in-phase and quadrature signal paths. Such in-phase and quadrature-phase (I/Q) imbalances introduce undesired image components in the baseband signal, degrading link performance -- most notably by increasing the bit-error ratio. Considerable research effort has therefore been devoted to digital techniques for estimating and mitigating these impairments. Existing approaches generally fall into two categories: data-aided methods that exploit known pilots, preambles, or training sequences, and blind techniques that operate without such prior information. For data-aided estimation, Cramér-Rao lower bounds (CRLBs) have been established in the literature. In contrast, the derivation of a CRLB for the blind I/Q-imbalance estimation case is considerably more challenging, since the received data is random and typically non-Gaussian in the frequency domain. This work extends our earlier conference contribution, which introduced a CRLB derivation for the blind estimation of frequency-independent (FID) receiver I/Q imbalance using central limit theorem (CLT) arguments. The extensions include a computationally efficient method for calculating the bound, reducing complexity from cubic in the number of samples to linear in the fast-Fourier transform (FFT) size, along with a simplified closed-form approximation. This approximation provides new insights into the allocation dependent performances of existing estimation methods, motivating a pre-estimation filtering modification that drastically improves their estimation performance in certain scenarios.