Not totally correct on the falling speed.
You need to consider any and all failure modes and have safety systems in place.
Hydraulic system could still have a cylinder 'break'. Cylinder splits down the side or the end cap blows off or blows out the seal and the fluid could just dump out there. Result would be a Rapid-Uplanned-Gravity-Powered-Event-Descent, or a RUGPED. Most people would just call it 'falling'.
You're over thinking this. Like an airplane, it's just not possible to have a backup system for a catastrophic wing failure. As a consequence, the elevator jack is over-sized, underloaded and inspected regularly, just like an airplane wing structure.
Not even a "real" elevator is designed to withstand a catastrophic cylinder rupture. At normal elevator operating pressures, the pressure within the cylinder tube isn't sufficient to open and propagate a crack far enough to allow a flow rate large enough to cause an injury inducing uncontrolled descent. Even if the gland nut seal, piston rod seal and cylinder tube failed all at the same time, the descent rate would not be large enough to cause injury at the pressures and volumes involved.
Elevator jacks incorporate a pipe rupture valve, however, In the event the supply pipe fails catastrophically, the resulting flow rate will trigger the rupture valve to shut.
Just like in aircraft, it's not the fall that is the problem. It's the sudden stop at the end.
I'm all for DIY. But this really isn't a DIY situation. IMNSHO. Even for A_Pmech.
Americans have become afraid of controlling their own destiny for fear that they are incapable of it, mostly because they have been told that they're incapable of it. Shades of Emile Durkheim in "The Division of Labor in Society?" I think so.
Instead, Americans choose to blindly abdicate their responsibility to the ignorant assumption that other people with "qualifications" have suitably designed, tested and approved a potentially harmful product. In my experience, that is a poor assumption to make. In fact, after studying several residential elevator designs, I'm afraid to ride in a "real" residential elevator. I'd like more than two pinion teeth engaging a rack lagged to a 2x6 wall between me and my destiny.
Single acting cylinder with an 8-10' stroke for a single-story residential elevator? Not an 'easy' item to buy or install. Hmmm, a 'full height' basement, then the big a$$ cylinder to power the lift platform from the first up to the second floor.
Surplus Center currently lists one 3-stage telscoping cylinder that could give you the 8-10' list range for a single floor/story extension. Item # 9-7848, actual full stroke is listed as 164", single-acting cylinder. Only $1300 plus shipping (520 lbs). Add in the control valves and hoses/piping and reservoir and pump and power source for the pump and the actual lift platform and the safety interlocks and the fall fail-safes (brakes and/or ratchet interlocks) and I'll bet that the construction costs are getting up there. That doesn't include any permit or 'certification' costs.
Remember that in general, man-lift required safety factors are 5-10x of 'rated' load.
Like I said, I'm all for DIY. In this case though, just go buy the dang thing.
Just like a "real" elevator, there's no need for a full basement, or any basement at all. Low-rise single-jack hydraulic elevators rarely require pits greater than 5' deep, including the hydraulic machinery space. They commonly use flange-mount jacks installed in cylinder pits.
Buy a cylinder? No way, I build them every day!