For a LWB: look at the Cycle Genius Falcon, about $1100. Upgrade the brakes: spend $200 more each to upgrade the BB5 calipers to BB7's. You will need longer handlebars as well, but the OEM's should work for a 5' rider. The OEM's are about 13" long and you'll need something around 18"+.

For an "upright" style bike, look at the RANS Fusion for $950. Not -quite- as comfortable as a recumbent, but is lighter, is just as easy to balance on as an upright bike and is still much more comfortable than a regular upright bike is.

I would advise against any bikes that have the pedals set higher than the seat. "Numb feet" can be aggravated by a number of things but is basically poor circulation to the feet--and a LWB recumbent is most-resistant to this problem, as the feet are kept lower than the seat base.

I've not owned a trike but from what I have seen, there's very few in your price range. There's only one Wizwheels that goes for under $1500; most of the big-name stuff like Greenspeeds is $2000+. And trikes almost all have high-set pedals.

A tandem is another option of course, but it's gonna blow your budget by a wide margin.
I love the concept of the Kettweisel delta trikes best, in that they can be used independently, or trained together. Each rider can have their "own" bike set up for them, but either can still be used to lead or stoke. This seems like a really nice thing to be able to do, but the Kettweisels are horribly expensive and I don't know any other company making cheap deltas that will work like this.

Also, ++ on the break-in period. You'd want at least a few weeks of local riding before you try such a tour on a radically-different bicycle.
~