I managed to get a $0.02 fee transaction (2.2 sat/B) confirmed after 88 hours (3.6 days).
Moreover, I put the dust to recipient at 1000 satoshis ($0.04)
(This cost will soon be $0.00 with the next update since the recipient address will be included in the op-return message)
The clue is that whenever mempool clears, miners include transactions almost no matter how low the fee is. After all, it’s in the individual miner’s self interest to include a tx and claim the fee rather than leave it for the next block’s miner.
When does mempool clear? Look at previous 10-20 blocks. Are a few of these less than 1MB? Then it’s likely the mempool is clearing and you can expect to be included in the next <1MB block.
If all recent blocks are full, expect to wait a long time. Mempool tends to clear when tx throughput is low (e.g weekends) combined with a lucky streak (sometimes lots of blocks are discovered within a short timespan).