@JoshD. 1st off my commiserations re your back. I had my 3rd back op in Dec 2015 and am "working" hard (special exercises, etc) not to have op No. 4.
I don't have an adjustable height bench (but several "lash ups" with different vices fitting one to another so I can - with a bit of a fiddle - get most of the work that I do in my shop up/down to a height that suits me.
BUT I do have an adjustable height "table" in my office. That uses screw jacks (one at each corner) that are "synchronised" by means of a bike-type chain and a sprocket on each jack. In my case, the bike chain is hand-wound with a handle, but electric versions are available (more expensive of course). The hand-driven one I have was expensive enough, and that was WITH a special deal I was able to get through the (Dutch in my case) manufacturer because at the time my wife was working on the fitting out of new offices for a company that was expanding rapidly. I seriously doubt that it would be economic to buy such a thing on "the open market" though.
I agree with Inspector that an "ordinary industrial scissor lift", hydraulic or otherwise, is likely to be somewhat less than 100% stable/rigid.
BUT (I presume you're doing regular physio at the hospital or a rehab centre?) Have a look at the "massage beds" the Physios use. I haven't looked closely but from glances, it seems they consist of an electrically-powered horizontal screw jack "scissor lift" mounted on a very stiff steel frame and working the bed frame up and down through a separate very substantial steel frame sliding on special "runners". Being in my hospital these frames etc are all heavily chromed, and as said, electric (to save the Physio having to use brute force to adjust for every different patient). But having been on one "a few times", and weighing in at 95 Kgs, I can say that these "massage tables" are very stable indeed, even when I'm required to make some considerable body movements for the various exercises.
I'm not suggesting you buy such a thing, they're big and heavy and like all medical stuff, they must cost a fortune. And I doubt you'd find such a thing second hand either. But I do wonder if a manufacturer of such beds would be prepared to supply just the horizontal screw jack parts, with you getting a local jobbing metal fabricator/welder shop to knock up the frames?
As said, I've never looked really closely at the massage bed I use, but I THINK only the horizontal screw jack (possibly a ball screw? and perhaps the 2 slide ways - linear bearings?) would be the difficult bits, with the rest being pretty straight forward, especially as we're talking bench here, and not something that needs to go into the clean hospital environment.
There is a firm called "Wixroyd International" who are manufacturers of various bearings, linear bearings, ball screw jacks, etc. I don't have a contact for them but they are in UK and MAY be of some help. I suggest a search for an on -line catalogue would be a good first point to start off.
Good luck (and with your back of course). BTW, I know every back is different, but at age 76 I've just started a new free-lance "job" at a local aviation museum (that's my professional background). Much to my surprise (and joy!) I've found that I can lead a group on a 90 minute on-foot tour around the museum WITHOUT back pain (but I do use a walking stick, mainly for balance - I have little feeling left in my feet so can easily fall - AND it's very useful for playing the sympathy card with the ladies too - but I digress). It all comes down (in my case anyway) to regularly doing all those +"*ç%&??!! exercises! STILL (twice a week). Horrible, but they work!
One final point, my wife got me a special "stool" so that I can stand/sit in/on for lots of jobs (not all of them) in my workshop. I posted about it at the time, I think about a couple of years ago now.
I'll close this post temporarily now, go look for my post about that stool, and come back with a link to add as a P.S. to this as soon as I find it. As said, good luck mate. Hope at least some of the above blather helps/encourages you.
Cheers