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TXsailor: That GPX rear derailleur will handle a 14-28 freewheel like the SunRace I'm using. But it's very picky about clearance. The 14 cog and chain just barely clear the dropout. I may try a 13-28 next, although technically that exceeds what Suntour said the GPX can handle.
Frankly I'd choose the desired gearing first based on rider preferences and not worry about trying to make the GPX group fit. Personally I'm annoyed by the GPX group more than satisfied. The rear derailleur on mine drags the entire drivetrain in the big chainring. I'd suggest swapping out the rear derailleur for a suitable long cage RD and toss the GPX into the parts bin.
It's difficult to describe but easy to demonstrate. On a functioning bike with GPX rear derailleur, put the bike on a trainer or sturdy workstand. With the chain in the small chainring spin up the rear wheel fast, then turn the crank by hand just enough to not engage the drivetrain -- you just want to feel the relative effort needed to turn the cranks without moving the wheel. It should be relatively easy.
Repeat this with the chain in the big ring. If it's like mine it will suddenly feel like the brakes are dragging or someone is putting friction on the chain. The angle and tension of the GPX rear derailleur create some unusual resistance to free spinning. Relieving tension on the p-knuckle pivot spring helps. This doesn't happen with other derailleurs I've tried, including an older Shimano 600. The GPX RD creates enough resistance to rob at least 5 watts and probably more. It's just a chore to ride the bike in the original condition in the big ring.
I've tried a few tricks to fix the problem but it's just a bad design.
Adding one or two extra links to create a little chain sag helps a bit. But it's not the ideal solution.
I'm modifying the RD to use lower tension in the p-knuckle spring (drilling an extra hole with a moto tool). Most rear derailleurs I've disassembled have two spring retention holes to set tension. The GPX had a pilot hole for the second hole but it looked like the factory didn't finish the job.
I'm also betting a smaller big chainring will help. I've ordered a 50T Vuelta chainring which should arrive next week. I ordered one last week but the vendor delivered a mislabeled 56T chainring, which I can't use, although a local friend can.
And I might shave a bit of material off the cage edges where it rubs the 28 cog no matter how I adjust the B-screw.
And if none of this helps I'll ditch the entire GPX group. The Accushift mechanism is extremely finicky anyway. Without the right freewheel, chain, etc., it won't index shift reliably. And the friction mode is mediocre. If adjusted for good shifting feel it'll creep and ghost shift. If I crank down the tension screw until it doesn't creep or ghost shift, the friction shifting loses any tactile feel.
After a year of messing with it I'm fed up. If modifying the p-knuckle spring tension and shaving a bit of material off the cage doesn't help I'm gonna dump the entire GPX group in a bin and start over with something else. I may switch to bar end shifters for my Ironman and put the older Shimano 600 group back on.
So I'd suggest doing that right from the beginning with your bike. Ditch the GPX derailleurs and Accushift downtube shifter. Find the gears your granddaughter wants and get the derailleurs and shifter to suit that.
Our turf around Fort Worth is pretty similar to yours, and I'm familiar with Bowie which is a bit hillier. My Univega Via Carisma has perfect gearing for this terrain: a 30/40/50 triple, a 7-speed 13-28 cassette (which I recently upgraded to 8-speed 12-32, even better). A Shimano Exage 500CX group and long cage rear derailleur. No drivetrain drag. It worked fine in indexed mode with the original thumb shifters but those wore out -- the holes that supported the mounting pivot pins eventually wore enough that the pins popped out. Rather than fix 'em I switched to Shimano bar end shifters which work great in friction mode (the index mode didn't quite match the MicroShift brand 8-speed cassette).
My Univega weighs right at 30 lbs as I ride it. We have a few short steep hills of 8%-11%, and occasionally I'll dip into the 30T chainring and 32 cog for minimal effort while climbing and it works great. Usually I'm in the middle 40T chainring and use the entire cassette -- doesn't appear to be any crosschaining problems. I seldom go fast enough to need the 50T big ring and 12 cog, although occasionally I do on some downhills.
Unless she really needs or wants a triple on the Ironman, I'd bet a 50/38 double chainring combo and 13-28 freewheel would do fine. I'm not a strong climber and the 39T Vuelta small chainring and 28T cog have been enough for the climbs I encounter locally, because the Ironman is lighter than my Univega. Otherwise consider a wheelset or hub for a cassette and try the MicroShift brand 8-speed 12-32, which is a good value at well under $20.