Starting Strength + Cardio

I'm female, chasing (or being chased by) 50.

My first love is running, but I need strength. I'm taking care of a lady now, who spent her life forcefully discouraging any exercise that took effort and now she can't pick up a soda bottle. I don't want to go there.

There is a grandmother in my gym who benches at least 200 and looks like she could deadlift a Buick. I don't want to go there either. I mean, I wouldn't mind ending up there, but I'm not aiming that high.

My perfect ideal would be to be able to, within five years, drop 20 pounds, do chin ups, deadlift 150, and bench 100. I think that's reasonable.

So, my hopefully not too crazy plan is thus.

Monday -- Cardio. Running most likely, though bike and elliptical are options.
Tuesday -- Rest day.
Wednesday -- Starting Strength with some light stretching afterwards.
Thursday -- Cardio.
Friday -- Starting Strength and light stretching afterwards.
Saturday -- Anything goes. It can be that Aaptiv workout with the elliptical and the hand weights. It can be a go at the rowing machine. It's a play day.
Sunday -- Starting Strength at an actual gym, followed a few hours later by whatever my gym buddy comes up with at Planet Fitness, probably that circuit thing. Not hating on PF, but they say they aren't an actual gym, and they don't let you deadlift. Deadlift is part of Starting Strength. They're highly likely to be my go-to fitness center for Saturday play day.

I'm starting slow (kettleball squats because I can't yet squat the bar with good form) and hope to make gradual, but steady progress. Currently, I can run 30 minutes six days a week, so I'm hoping trading those days will work.

Does this sound crazy, or viable?

Thank you.

-Ivy