I hear you. I know BEANS about electronics but using an arduino, a resistor, a Mosfet and a heat sink is something you can look up online and educate your self in well under an hour. You don't have to know it all. I have just been learning for about a year and discovered a few incredibly basic things that have opened up a whole world of things I have wanted to do for years. Simple things like Voltage dividers that require 2 Resistors are so simple it's laughable BUT, when you don't know about them, it sure blocks a lot of options.
I too am comfortable with electrics. Played with batterys and wires since I was a kid. Now set up my own solar systems with over 20KW of panels, Play with generators, IMAGs and everything else. I understand the difference between electrics In wiring stuff up and electronics real well. Just like I can do pretty much anything around the Hose with electrics, I woudn't want to go try wiring up the switchboard in a factory.
Same with electronics. The basics allow you to do a lot of things but that's different to building your own 5Kw Inverter... which lots of the Geniuses do all the time.
I have wanted to do Direct solar water heating for a few years. All the commercial options are Bull$#|+ expensive and pretty marginal in a lot of cases. I'm now Modifying existing boards with a few components which are working perfectly and one of the gurus designed a circuit and board which is very simple which I have built up and am testing with a view to offering the things for sale. They will handle KW's of power at mains voltages on mains elements where a lot of things out there now are really have quite pathetic power handling and are more toy than practical despite their often $500-$1000 price range. The one I built is bare bones as it comes, No monitoring ( other than a flashing indicator Light) No bells and Whistles, easy as anything to build like a kids Kit and just enough to drive a resistance element with huge power handling and excellent efficiency and not a thing more.
Like I said, I know beans but I have learned a few of the very basics and that makes a HUGE difference to what one can do. There is a LOT of info on the net but if you can get the help of some of the electronic Geniuses out there on forums, that is an asset to behold in itself. I have found that a lot of these Gurus are retired people and if they see you are interested, prepared to do your homework and put in some effort, they are VERY helpful people indeed.
When ever I ask a question I try to put in my thoughts and the reasons why at the same time,. this shows I am trying to understand and they can then correct or confirm what I'm thinking. I can't design anything but the most rudimentary circuit but I can modify things to suit what I want and although my knowledge is extremely Limited to the area of Interest I have, Power control, just understanding the theroy give great insight as well.
I know one can look at it and Not understand a damn thing and be frustrated as all get out but If you stay with it, things will drop into place pretty quick. Look up things like PWM ( Pulse width Modulation), Mosfets, Voltage dividers, Rectifier Bridges for a start. That will all be relevant to what you want to know and get you going.
As for how things were done 50 years ago, I don't have a clue. I also suspect that both this type of thing was not done anywhere but an industrial scale and would be too expensive now and that the components would be hard to get. You mention transformers but the last time I looked, to get a transformer of that power handling you want would be expensive, probably hard to get and weight a ton and therefore cost a bomb in postage as well.
OTOH, using a pre built PWM controller and a mosfet or 2 Will be readily available, Cheap, small and compact and do an infinitely better job. You could also find endless designs on the web you can strip down ( as most will be overly complex) and just build something really simple.
I modified the most simple Arduino program of all which makes an LED flash on and off and built a real simple circuit off that with 4 Components and it runs one of my solar heater designs and would be entirely suitable for what you want to do as well. Would have the exact parameters you want to give you full voltage at reduced Current. That's what PWM primarily does.
It's not hard as it seems either. You just have to be willing to learn. I'm thick as 2 bricks and things don't sink in to easy but this stuff is no where near as difficult as the overwhelming thing it seems. Idea is to take little bites, not try to rebuild your television set after an hours reading.
A transformer will work by limiting power and causing the voltage to sag. You turn up the power and the load voltage is pulled up.
In between there is a lot of heat and wasted power. I don't know how to control the amps by capacitors but in playing with Induction motors and converting them to generators, I have a feeling the size and rating of the caps you need are NOT going to be cheap.
Plus again it's really inefficient and ugly way of doing it.
I think if you put in a bit of learning time you'll probably be able to do this faster than find a conventional solution and a lot cheaper as well.
Give it a go. Not as hard as You might think and certainly not as hard as I thought.