If your current cogset is a freewheel it probably has no more than 7 cogs which limits the number of different gears.
How many gears you need depends on your own preferences: how high a high -- you've said you want a higher one and yes, 70" is pretty low; how low a low -- with the 24/34 I assume you want to keep a similar low gear of <20"; and how close you want the gaps between gears.
The possibilities also depend on how often you shift between chainrings and how much you like quick, smooth shifts.
The easiest option would be to swap the 38 for a 46 which would give a still pretty low 85" gear, assuming a more or less 26" tall wheel. The gap between this and the 24 is pretty big but it has been done, and it would be more doable if you don't use the 24 very much.
The next option is a triple with 46/36/24 which is pretty typical 7 speed triple chainring, tho' still on the low side with 26" wheels. Or -- my preference were I to use a triple with 5, 6, or 7 sp fw -- would be something like a 46/42/24 halfstep plus granny for closer ratios with higher top and same low.
But my overall preference would be to go whole hog and swap the hub for a modern cassette hub with 10 or 11 gears; yes, you'd probably have to spread the rear but it's not hard to spread a 126 mm OL rear to 130; in fact, I've often used 130 hubs in 126 steel frames, tho' it's a pain. With 3 or 4 more cogs you can (1) mix and match much more easily, (2) get a much higher top gear with the same 38 t ring, (3) get a similar or even lower low, and (4) get closer intermediate gears, and (5) do this without adding another chainring.
I personally like "1X + granny" using 10 sp cassettes (might one day try 11) with something like a (note: this is for 700C wheels with fat tires, so about 29" tall, 3" taller than 559 wheels) 44/28 and a 14-28 10 sp (easy to customize cogs with a freehub) giving a high of ~90" and a low about 29", but with very close intermediate gears. Abandon 1-cog differences in the cruising gears and you can get just about any reasonable high and reasonable low with this sort of setup.
Patrick Moore, who has owned umpteen gadzillion 26" wheel road, all-rounder, and mountain bikes each with customized gearing. (My 2 current 26-ers are road bikes -- 29" for off road -- one fixed or with 2-speed IGH fixed hubs, 76" and either 68", 66", or 57" depending on hub) and the other with 3 speed fixed: 72", 65", 54" or 3 speed fw: 75", 65", 56"; 24.5" 559 X 28mm and 25.6" 559 X 42 mm wheels respectively, but I've used singles, doubles, and triples on various 26" wheel bikes.)