Options 2 and 4 are both very appealing; but I am leaning towards Option 4 (hence my current vote).
Science is good, I love it. Yet we currently are covering enough of that with PODC, I believe.
RandomX will definitely provide us with a lot of exposure at this stage. Monero network hash rate soared from 800 MH/s to 1.2 GH/s in a month - this corresponds to several hundred thousand cpus running RandomX, even if some of them are latest Ryzen 9s. In most parts of the world, a typical 5-year-old cpu is barely breaking even at current network hashrate. Those miners would simply jump over a side benefit such as merged mining of BBP, once they are made aware.
If I am right in the sentence above, then we would see a huge spike in difficulty of BBP POW - old timers or hobby miners may kiss their BBP rewards good bye. This needs to be prevented, imho.
Another concern I have is the flippers: many of those RandomX miners that start mining BBP will prefer to liquidate BBP first, to cover some of their expenses. Remember when we could earn Obyte, Neumannium and a couple others on the side last year with PODC? I doubt anyone kept, say, their Neumanniums
I believe this possibility has to be taken into account (better ready than sorry, right?). The only precaution I can think of is incentivising hodling of BBP (or soft-penalising of liquidation). Coin*age requirement as in the ABN times, or proportional PODC RAC requirement for POW rewards, or even fiat donations to charity required for POW rewards, you name it. People that have to pay up front for a reward will be less likely to sell it at any cost (which kills the market).