Optimizing crawl budget for large sites

I'm currently knee-deep in a comprehensive technical SEO audit for a massive e-commerce platform, which boasts millions of unique product and category pages. It's an intricate beast, and while we've made significant strides, we're still grappling with some persistent issues.

My core problem is that despite implementing a wide array of initial technical fixes, we're consistently observing highly inefficient Googlebot crawl behavior. This isn't just a minor inconvenience; fresh content and critical updates, which are vital for an e-commerce site, are experiencing unacceptable indexing delays. This clearly points towards a suboptimal allocation of our crawl budget, which for a site of this scale, is absolutely critical.

To tackle this, we've already taken numerous actions. We've meticulously optimized all our sitemaps, ensuring they're clean, up-to-date, and accurately reflect our canonical URLs. Our robots.txt directives have been refined to block irrelevant sections and parameters. We've significantly improved server response times across the board, which was a major undertaking. Robust canonicalization strategies are in place to prevent duplicate content issues, and we've heavily invested in enhancing our internal linking structures to ensure deep content discovery. Basic duplicate content issues, especially those arising from product variations or filtering, have largely been addressed.

However, the real technical block now is moving beyond these foundational improvements. We need to identify and systematically eliminate more subtle, insidious forms of crawl waste that are still eating into our precious crawl budget. I'm particularly concerned about issues related to dynamic URL parameters that aren't properly handled, the complexities of faceted navigation creating endless crawl paths, inefficient pagination schemes, and the heavy reliance on client-side JavaScript for rendering critical content. My strong suspicion is that Googlebot is either spending far too much time crawling non-valuable, non-indexable URLs or struggling significantly with the rendering process, leading to missed content or delayed indexing.

I'm now actively seeking advanced strategies or methodologies to gain more granular control and insight into Googlebot's crawl budget expenditure. Specifically, I'm very interested in sophisticated log file analysis techniques that can pinpoint exactly where Googlebot is spending its time, server-side configurations for more intelligent crawl prioritization, and cutting-edge JavaScript SEO rendering strategies that can prevent crawl traps and ensure efficient resource allocation, especially for SPAs or heavily JS-driven pages. Are there specific tools or processes, perhaps even custom server modules, that can offer this level of control and insight?

I'm eager for expert-level guidance on tools or processes that can help us diagnose and rectify these deep-seated crawling inefficiencies. Any insights from those who've tackled similar large-scale crawl budget challenges would be immensely valuable.