The balance between neural excitation and inhibition (E/I) is crucial for cognitive functions such as memory formation and retrieval. Disruptions in E/I balance are implicated in neurodegenerative diseases like Alzheimer's disease (AD), where neuronal hyperexcitation has been observed. We present a novel multimodal model that integrates resting-state functional MRI and diffusion-weighted imaging to recapitulate functional and structural connectivity dynamics with high fidelity (citations omitted: double-blind review). This model provides a whole-brain, systems-informed measure of excitation-inhibition levels, enabling the investigation of E/I balance in human studies. In this longitudinal study, we analyzed data from 106 cognitively unimpaired older adults over multiple time points. Using our multimodal connectomics approach, we constructed individualized resting-state structural connectomes (rsSC) that capture both functional and structural connectivity. We computed a whole-brain excitation-inhibition ratio (EIR) for each participant (see Additional Details). Linear mixed-effects models revealed a significant three-way interaction between time since first scan, sex, and APOE-$\varepsilon$4 status on EIR (p = 0.018). Specifically, female APOE-$\varepsilon$4 carriers exhibited a significant increase in EIR over time (p = 0.042), indicating a hyperexcitable trajectory not observed in male carriers or female non-carriers. Our model's high fidelity in capturing connectivity dynamics (both structural and functional) strengthens the validity of these findings. These results suggest that female APOE-$\varepsilon$4 carriers are at higher risk of developing neuronal hyperexcitation, potentially contributing to their increased susceptibility to AD. Our systems-informed measure of E/I balance could serve as a potential biomarker and provides mechanistic insight underlying sex- and genotype-specific AD risk. Moreover, identifying underlying hyperactivity opens avenues for using antiepileptic treatments, such as levetiracetam, to restore E/I balance, preventing or slowing the progression of AD in select high-risk populations. This work underscores the importance of incorporating computational models to develop personalized preventative therapies targeting E/I balance alterations in at-risk populations.