How to sleep on an overnight layover in Kotoka Airport, Accra

I'm considering options for a difficult flight route. One of the best options (no, really) involves a beast of a 14-hour overnight layover in Kotoka International Airport, Accra, Ghana.

This is awkward because:

• To leave the airport and go to a hotel, I'd (UK citizen) need a visa. Ghana seems to expect visa applications from your home country, which isn't logistically possible for me, requires a letter of invitation, and doesn't appear to normally offer transit visas, so a regular visa doesn't seem to be an option.
• I've seen 3rd party reports suggesting you can sometimes get a 48-hr transit visa at the airport for $20, which would be fine, but I can't see any official confirmation of this or details on the requirements or whether it's possible to apply in advance.

• According to Sleeping In Airports.net there are no rest zones, and:

  There are a few hard benches available. Your other choice is the cold, hard tile floor. Have a travel mat or sleeping bag handy for added comfort!

  ...which isn't great.

• It also says there are three airport lounges, of which one is apparently 24 hour, but it's not clear whether it's possible to pay to use this lounge and says there's no sleeping facilities, so I'm not sure if it's possible to sleep there. Diners Club suggests it has a 4-hour maximum stay: presumably if they're watching how long you're there, they won't take kindly to sleeping.

• There are plenty of hotels very close to the airport, but it doesn't look like it's possible to reach any without passing immigration.

• I've seen various threads on this topic on trip advisor, lonely planet, etc and they just fill up with other people asking the same question, or commenting on how little there is to do at Accra airport. No-one seems to have any answers. I saw one comment from a Swede (can't find it now to link to it) saying they got temporary papers allowing them to go to a hotel, but it could be that Swedish citizens get a better deal because Ghanaians get a better deal from Sweden.

What can I do if I have a very long overnight layover in Accra, want to sleep, and don't fancy sitting on a hard bench for 14 hours or lugging around some kind of portable bed (which I'm not sure they'd even allow)?