Solomons to PNG

I know you can get from PNG to the Solomons, but can you go the other way without flying? Can you get a PNG visa in the Solomons? Anybody?

There is a PNG High Commission (ie Embassy) in Honiara, so you should be able to get a Visa there. I don't know how long it would take, my advice is: don't hold your breath.
However, depending on where you are from, you may only need to get it when you enter PNG.
There is one flight a week from Honiara to Port Moresby. There have been experimental flights to other parts of PNG, but I don't think any are happening at the moment.
If you want to cross overland, or actually by boat, I am not sure what the deal is.