Exceeding the chainwrap capacity of a rear derailleur can be done safely and effectively, with a couple of caveats:
A couple of teeth over is all you're really gonna get, and size your chain so that the big/big works. It doesn't have to work all that well, but you need to able to shift the bike into it and not have the drivetrain lock up. Cuz that's a really nasty crash and a broken bike if it happens. I've seen it. 'Twas ugly.
That said, you're on the right track with your math.
(12-28) + (48-26) = 16 + 22 = 38, so 4 teeth more than the 34T chainwrap of your derailleur. 4 teeth is a lot when pushing specs like we're doing, I like to limit it to 2 so that everything just works. In that case, you either need to lose 2 teeth on the top or gain 2 at the bottom. 48x12 is a 105.83" gear, 26x28 is 24.60"; 46x12 gives 101.33" and 28x28 is 26.46", so your choice is lower high or higher low. Me, I'd go with the lower high, but I'm old and slow. YVMV. (Your Velocity May Vary.)
Your short-cage rear derailleur also has a 16T difference-of-chainring spec, which determines if the chain will clear the tail of the front derailleur in small/small. Yours won't. With a 46/26 or 48/28, you're at 20, so we need to get 4 teeth back somehow. 12 + 4 = 16, so you won't be able to ride the granny in any cog smaller than a 16. If you do, you'll hear it, and if the chain jams on the FD, bad things may happen. 48-26 is 22 teeth, which is too much, IMNSHO.
"Short cage on a triple" is a venerable and worthy setup, but there's compromises. (There are always compromises. TANSTAAFL.) If you haven't already bought the rear derailleur, just buy the medium or long cage one and don't sweat any of this. The Miyata 1000 is a touring bike, after all, and would have come with an MTB rear derailleur. (If it were my bike and my money, I'd put a 9-speed XTR on it... plentiful, cheap, and fantastic!)
--Shannon