Again, you're looking at a 3-way match between cassette, shifter and derailer.
If you stay within the Shimano family, most rear shifters are compatible with most derailers as long as the number of sprockets match the number of speeds in the shifter. There are some exceptions though.
Your biggest hurdle will be that road front derailers have another actuation ration than MTB shifters. And MTB derailers tend to be a bit unhappy having to deal with the bigger chainwheels used on road bikes. They may also have the cable pull in another orientation.
If you were to get a MTB brake/shifter combo, then it's probably intended for v-brakes, which also have another actuation ratio than "road" caliper brakes.
The easy and elegant approach is to buy flat bar road shifters/levers
http://techdocs.shimano.com/techdocs/blevel.jsp;jsessionid=QPzlTpGW229tPHRQQv7mrQSnlJHsvxNtTHDMm55spytfVqJvrGjx!-1786427113?ASSORTMENT%3C%3East_id=1408474395181679&FOLDER%3C%3Efolder_id=2534374302051115&bmUID=jbZOmqC
With a nice frame, this'd be my option.
Or you can get a right rapidfire unit for the rear shifting, a left thumb/friction shifter for the front, and some appropriate flat bar canti/caliper brake levers.
Here's a link that may be helpful:
http://www.ctc.org.uk/desktopdefault.aspx?tabid=3946
Even if Miami is decently flat, I still wouldn't go for downtube shifters.
In my book, shifting is GOOD, and should be made easy. With DTs, I'm a lot more likely to stubborn it out rather than shift, which my knees don't appreciate at all.
Granted, drop bars may be a bit of an acquired taste, and if you've decided you don't want that - good for you. You should have the bike the way you want it. But if you're OK with Rapidfires, brifters aren't that far away. You'd be able to transition in no time.
If you want vintage, get another bike instead. If you're happy with just the look you should be able to pick up a period perfect bike fairly cheaply by hitting a few yardsales. New tires, cables, perhaps a chain and a lube job and you'll be rolling again.
With a modern frame. flat bar and DT shifters, the bike would be a bit of a mongrel anyhow. You could get some psuedo vintage look going if you used a moustache or a North Road bar.
You may want to look for a smaller chainring/crankset. With a flat bar, you won't really need a 50+ tooth count as a biggest ring.