Perhaps a variation on this approach would be interesting: limit the weak block cache based on the size of transactions (skipping duplicates), and have it be relatively high rate, say 16x. Then you’d almost always have txs from a recent block generated by any mining pool with 10%+ hashpower.
The downside to that approach is that given the poisson intervals you’d “often” have 50 or 100 weak blocks between each real block, and you’d “often” get weak blocks being found only a few seconds after the previous weak block. (“Often” in this case is “once a day”) That probably just means you want to be able to process weak block messages very quickly; but if you’re only validating PoW and stuffing the contents into a cache, that’s probably okay?
This would probably be interesting to run on signet: both because it’s easy to get 100% miner coverage, and because inquisition means there are actually meaningfully divergent mempools (eg).