The constant stop and go, and low-speed operation of a rural mail route would be ideal for a hybrid, but you probably don't have the budget for that. I don't think it's practical to turn a left-hand-drive car into a right-hand-drive -- the whole steering business will have to be replaced, and then there's moving the instrument cluster and the floor pedals. To do it right could cost a lot of money. Rural carriers around here appear to be using unmodified cars and trucks (A/T, of course) and just stretch to reach the wheel and the left foot for gas and brake. Not terribly safe, I'd guess... a bench seat and no floor shifter would be necessary. Any chance your spouse or S/O can share the duties and do the driving itself? They'll have to get used to coming in close to the mailboxes without clobbering them! Maybe you can work out some hand signals.
Car designers are talking about having just a few platforms (various advanced vehicles) that you plug in the instrument cluster, electric steering, and pedals. That's a few years off, but would make it easy to shift back and forth between LHD and RHD!
I've seen a RHD car or two (Subaru, I think) in the area, so they must be street-legal. Go ahead and ask various Japanese car dealers about it, but don't be surprised if you pay a big premium (and the controls may not be in English, and maintenance may be a problem/expensive). Have you asked the Postal Service if there's any way to obtain surplus RHD mail delivery trucks? Maybe they'll be worn out, and it may be hard to get someone to work on them (platform?), but it's something to consider.