Bitcoin without internet: (for context)
I am considering the synchronization of a node to be partially solved by the BlockStream satellite that broadcast blocks and transactions.  It is centralized, but certainly better than nothing.

It is possible to "broadcast transactions" via radio.  It's been done with HAM radio, and perhaps on other radio bands too.  It does requires someone to receive it and relay the transaction to the internet, but that is unavoidable.  More importantly, radio waves are regulated making it a legal challenge.

It would be easy to setup "base stations" that listen to [some frequencies] and relay any valid transaction that it receives to the internet.  As far as I know, there is no such active relay, though I believe it would be totally legal in most countries and, even where illegal, it would be very difficult to track/down such relay unless they advertise their location.

I have heard of the goTenna, which has some interesting tech for broadcasting transaction.  I don't see how that can be helpful for mining, but looking into it can certainly give some insight.

While far from perfectly reliable, but definitely a suitable backup, one could transmit transactions via SMS.  Now that I think of it, there are a bunch of free services to receive text messages on disposable/temporary phone numbers in most countries across the world.  They could be monitored and valid bitcoin transaction relayed to the Bitcoin network over the internet.  It would take a couple separate messages per transaction, but that could be done.

Solo mining:
To limit the bandwidth required, some scheme may be used to per-determine which transactions are to be included in a block at any time, e.g. relying on what BlockStream has broadcasted up to some time in the past.

For a solo miner, assuming the BlockStream satellite is operational, we only need to "somehow" broadcast at most a couple hundred bytes to a relay (connected to the internet) and that's it.  Given the blocktime, a solo miner can send a SMS for every block found.  Using radio waves is also a potential solution, though legally more complicated.

Pool mining:
For pool mining, as far as I know, the bandwidth required is way too great to use SMS.  I don't like the idea of using SMS in the first place anyway, but that excuses only applies to solo mining.

As far as I understand, shares are submitted to the pool very regularly, i.e. a great handful of times per minutes.  Could it make sense to send the few best shares per block and send that only after a block is found?  It seems to break any payout scheme that I know.

Mining farm can aggregate their mining so that they appear as a single worker to the pool, but that is far from enough.

Using radio-waves (to broadcast) is a legal challenge to start with, and there are a LOT more shares to transmit than there are blocks.  Even with the ability to have each farm send only a few hundreds or thousands bytes for every block, ALL farms would be broadcasting their "few shares" almost at the same time, i.e. when a block is found.

Mining without internet:
Mining cannot afford the propagation delay that transactions do.

The idea is to have a fallback communication network for mining in case of an internet outage.  But during an internet outage, a nearby relay is likely experiencing the same internet outage.

One or a few mining farm(s) going offline for a couple days is not that big of the deal, except for the operator(s).  A backup solution is certainly helpful to such miner, but not critical for the network as a whole.

After much solo reflection, for anything more wide-spread, it seems that such a backup network can only be useful if it actually handles most mining communication.  i.e. if it "can" handle the load but waits around until internet breaks, then we should expect to discover its fatal flaws when it gets under load.  I am mostly thinking about pooled mining.

I swear I din not intend this post to go that far, nor that deep.

That said, maybe BlockStream is even less ideal here and node synchronization has to be addressed just as well.

Summary:
How to enable mining farms and residential miners to keep mining during local, regional or global internet outages?

What communications channels can be used for communication?

How can the bandwidth required for pool mining be reduced?

As a final thought, it appears that a solution for offline mining may well be a solution for sending and receiving transactions without internet.  I hope, however, that I made clear that mining is a different beast.

Do some mining farm and/or mining pool have any sort of private or backup communication channels for blank swans or in the event s..omething hits the fan?