You can take the guesswork out of string gauges by using a string tension calculator. You're using stringjoy strings - why not use their string tension calculator, which is specifically designed for their strings -
https://tension.stringjoy.com/?
Typical "nominal" string tensions for lap/console string sets are around 30 pounds per string - plus or minus whatever you like, and sometimes there are good reasons to go over or under - e.g., if you just like a lower or higher tension, or want to pull a string. For hi-lo G4-E4-C4-A3-G3-E3-C3-Bb2, that yields around 12-13p, 15p, 18-19p OR 18-20w, 24w, 28w, 32w, 42w, 48w - these are slightly heavier than 30 lb, go a gauge lighter for a little lighter than 30 lb.
I assume 54 and 70 for the bottom two are for an octave lower - the tensions at C3 and Bb2 are around 51 and 67 pounds, respectively. They might not break, but that seems unreasonably high to me. But I get around 13 and 17 pounds for the octave-lower C2 and Bb1, respectively. Those would feel real floppy to me, but if one is going for a floppy baritone guitar type of feel, that might work.
As far as breaking strings go - that .010 for G4 should in principle tune up with no problem. But light strings at high tension are more sensitive to imperfections in anything. Issue with string, burr in nut or saddle, pulling a string too hard, whatever. Tension is around 20 pounds for G4 at 22.75" scale, which is light to my tastes also. Even pedal steel at 24-24.25" scale typically uses .011, .0115, or .012 gauge strings for G#4, which is bent up to A4 constantly. Of course, that is the pedal steel string most likely to break. But .010, even at the longer scale, sounds very thin to me. I don't know anybody who uses .010 for pedal steel G#4, although I imagine there are some players who do.
In general, within reason, increasing string gauge from a reasonable nominal tension at a particular pitch does not necessarily increase string breakage. The reason is that although the string tension goes up, so does the cross-sectional area, and thus the tensile strength, of the string. There is a point in the string tension vs. gauge curve where it becomes very nonlinear and the tension starts going up much faster than the tensile strength and the string pretty much always breaks. But I often find that moderate increases in tension actually reduce string breakage. For example, I run some Telecasters with a 12-52 set with a 20p third so I can still bend it a whole tone with no wonkiness. I have never, ever broken a string on those Teles. I would break strings with 9-42 sets all the time, 10-46 sets periodically, but almost never break strings on 11-48 sets. Heavy strings are heresy among many if not most electric guitar players, but I set gauges for these 12-52 sets at around 25-26 pounds per string, and they play just fine, can be bent with no problem, permit rapid alternate flatpicking as on an acoustic guitar, and never break, at least in my experience.
BTW - looking at your photo, I read hi-low 14, 15, (17 or 19, hard to tell for sure), 20p, 24w, 30, 54, 70, not 10, 14, 15, 20p, 24w, 34, 54, 70.