I heard bitcoin-core 0.11 allows 80 byte OP_Returns, but I know miners operate different implementations and was wondering when it would be likely that 80 byte OP_Returns will be swiftly included in blocks.
As you can see, only 10.8% of nodes have upgraded to 0.11 and 29.3% of nodes use a pre-0.10 distribution. (Source: https://getaddr.bitnodes.io/dashboard/#user-agents)
Considering that we don't know the hashing power of these nodes and don't know your definition of "swiftly included", there's no way to exactly answer your query.
However, if you assume hashing power to be equally distributed between nodes, There's about a 10% chance that any give block will be mined by someone running 0.11, so about a 47% chance that a 0.11 block will be mined at least once an hour.
I remember having the same question when the initial OP_RETURN ability came out in Bitcoin Core 0.9, but most of the network was still running 0.8.
I remember that it began to be reliable to send OP_RETURN transactions and get them mined once around 30% of the network was willing to relay them.
So you should keep an eye on https://getaddr.bitnodes.io/dashboard/#user-agents for a similar %age.