4'12" is 5'...so plenty of bikes should fit.
A month ago I sold an 80s Raleigh road bike to a woman who was right at 5' and it was a 48cm measured c-t.
Save Up to 60% Off Touring Bikes | Commuting | Commuter Bikes | Motobecane Bikes - Gran Turismo for touring the country there is nothing better GET THIS! the 43cm bike is still in stock and itll pay homage to your country's cycling heritage...or insult everyone...either way.
Name aside, its spec'd really well and the 43cm with a 28.5" standover, which I would guess is pretty close to what would be needed.
Bob Jackson Cycles
This is a frame I would love to build up. Its 900 euro for the frame and fork though. Well above the listed budget, but its steel, quality made, very individual, and comes in 47cm.
Anyways, there are a lot of bikes that would fit and worst case- get a soulless LHT and have fun.