How about a cyclic sine sweep?
Experiment to find the highest & lowest frequencies the phone can comfortably repro, then sweep between those 2, low to high then back again, then loop.
Pick a sweep frequency you wouldn't confuse with a passing fire/police/ambulance siren. There has to be some good reason they use sweeps too.
Late thought - you could actually do 3 versions - constant cycle, low to high & high to low, for 3 different purposes.
idk about other phones, but iPhone ringtones tend to peak at I think -10dB, so you can push a little bit on the volume without damage, but as you rightly point out, peaking near zero just goes quickly into distortion; doesn't sound good & actually doesn't feel as loud from a distance.
Alternatively - & this is what I use for my partner's ringtone - the telephone ring from the Keifer Sutherland show, 24, the one in their office at CTU. It changed each season but the early ones were the most distinctive. Fox used to have them freely available on their website, though I don't see them any more - but a quick Google tells me you can still pick up one or more versions for free.
For me, maybe it's just familiarity, I've had the same ringtone for her for over 10 years across many different phones, but it is one I can hear right through the house.
Music, snippets from songs etc., don't work well - they just seem to blend into the background too easily, especially if you've got the radio or tv on.
The only exception is if the music is very sparse. I use the opening 2 chords from The Clash, London Calling, for one of my ringtones & I can always hear that round the house where other tunes don't work - though I have been known to come dashing up to my work room to discover ...it was the radio.