Actually, here's what I came up with from your scenario.
Assuming you dive a 60' perfectly square profile (as in, no time spent descending or ascending), and you stay there for 60 minutes, and you do a 5-minute stop at 15', and you end up with 500 psi in an Aluminum-80 originally filled to 3000 psi (giving 77.4 cu ft of air), your surface air consumption rate (SAC) is about 0.366 cubic feet per minute (cfm).
On a dive at 130', assuming you were still breathing your very respectable SAC and were not at all stressed, you'd need 4.71 cubic feet of air for the ascent at 30 feet per minute plus 2.66 cubic feet of air for a 5-minute stop at 15'. That puts you at 7.37 cubic feet of air to end the dive under normal conditions, which means the 6 cubic foot bailout is woefully inadequate -- if you're going to your bailout, you're almost certainly not under normal conditions, and you're almost certain to be stressed.
The 13 cubic foot pony is enough to get you from 130' to the surface, including the 5-minute stop at 15' you mentioned, assuming your stress level doesn't increase your SAC beyond 0.645 cfm. A 19 cubic foot pony would allow you to reach the surface at a normal ascent rate, including your 5-minute stop at 15', even with your SAC bumped all the way up to 0.943 cfm. If the dive's really going south fast, having your SAC double or triple isn't unheard of, and even if it doesn't, for every bit of additional air, you have more time to fix any problems before you become S&R practice.
6 cubic feet just plain isn't enough, unless you blow your ascent rates and skip your stops, which will certainly make a chamber ride much more likely to be necessary. 13 cubic feet will get you up, but if complications arise, you may have to blow the stop or trash your safe ascent -- it's better, but it's still tight enough to be unsettling. 19 cubic feet gives you the 6cf on top of the 13cf, which should give you time to handle a problem like an entanglement (say, like the one that cut your primary hose in the first place), while still making a safe ascent and stop(s). Plus, the difference between the 13cf and the 19cf is just a little length (they're the same diameter), and that's all but irrelevant. For 50% more emergency air, I'd go with a 19cf, for sure.
In fact, I did, and I carry it on all my dives.
(Postscript: If you were stressed enough that the 13cf pony would *just* be enough to get you to the surface at the normal safe ascent rate and including your 5-minute stop at 15', at that stressed SAC rate, the extra 6cf would buy you an extra 3:18 (three minutes and 18 seconds) at 130' to solve whatever problems you need to solve before you can start ascending. Is that worth a couple inches and really just a few bucks?)
