Thank you, all.
I suspect that all of the above will help other handloaders who, like me, have very limited space (and possibly limited lifting ability due to age and/or misadventure!). I'll claim the misadventure bit, since 70 ain't that old when you compare it with, say, the mountains in Yosemite.
As for me specifically, I can't see bending over and lifting heavy stuff, but I have decided to bypass the Lee kit, which probably is not as sturdy as that MEC plate that I viewed online.
The press on the right (Lee Turret) is indeed mounted on a steel plate bolted onto the sturdy wood cabinet, to offset it from the drawer behind it.
After cogitating on your answers, I'm going to follow the great advice of several here and have a heavy steel plate machined for each of two presses (Rockchucker and future Hornady AP), use existing holes or mate new holes to the plates and use wingnuts and washers (facing up for ease and speed) for whichever application needed. I like having my permanently set .44 Mag progressive press where it is, since that is generally what I shoot. And I still like the super quick change of the preset turrets for small loads on the Lee Turret.
I decided on getting a Hornady AP Lock-n-Load, for several reasons. I don't like the fact that I'll have to shell out around $38 for each of the unique shellplates - 45 calibers, 357/38 calibers, other pistol and rifle calibers. But otherwise, the price is still pretty amazing for what you get. Here is why I like this press, after much research which included a lot of helpful comments on this forum:
* I insist on hand priming each round. No jams, no fussing with changing tubes and cleaning them, no repriming if a progressive load gets stuck. I can be sure that the primer is set in properly. It gives me something to do inside with my wife while we watch something on TV or talk.
* But - putting each case into the single-stage (Rockchucker) or turret (Lee) press and then taking it out just to size or size and deprime it is wasted motion.
So, with the Hornady:
1) Its quick Lock-n-Load system allows you to use only the sizing die without having to reset the dies later; they are locked into their rings and removed by twisting and unclicking. I can put in a case, pull the lever, put in another case, and so on - without removing it. It is walked around the carousel and dumped into a container, saving a great deal of time and motion. T
Checking the various posts here and several YouTube videos, the Hornady ejection system is not perfect but it is actually quite good - with a simple spring that surrounds the shellplate that holds the rounds.
2) The quickest changeover for loads except my Lee Turret. Once dies are set, you just lock them in for a load.
3) Since I size and deprime separately, I can remove that die and use the 5 stations with more freedom. I can use a Powder Cop die to speed up the process, insuring that there are no light or heavy dumps.
4) Bullet types within a caliber are more quickly adjusted because I don't have to set a crimp. I can place my Lee FCD for that caliber in the extra station. With my current progressive setup, I crimp on the other press because of the same reason - quicker changeovers (setting) for different bullet lengths, and a consistent crimp every time.
5) And incidentally, I like that the powder dispenser only works when there is a case in the revolving station - no having to disconnect the dump arm while setting up the first two stations. Very cool.
I guess this sounds like an ad. But perhaps the above will be helpful for other folks starting out in handloading. If the press turns out to work as I think it will, I will be selling a lot of Turret stuff - and the Lee press - at very good price to somebody; it sure would save a lot of space.
Close-up of some turret setups in cabinets above presses