Beat trainers
 

I have a theory.

You get stronger with a certain type of bike. I had built myself out of necessity and on heavy budget constraints a bike of this type for all my transport needs this summer ("power commuting" as I call it) . I ended up doing a time trial with it and getting a pretty good time (considering full carbon/full dura-ace bikes were in the lead)

The frame has since been crashed but let me talk about the setup which I will reproduce on first sight (of suitable beat frame).

The frame was perfect for my height and had race geometry
It was a lugged 83 Peugeot Course (PB-12) with Carbolite 103. We all know this is heavy metal. The rest was a mish mash of found parts or bought for dirt cheap. Mid-to-low-range vintage stuff.

The most important thing might be, though, that it was a single speed setup with a 52/16 ratio.
This forces you to crank all the time...
You get better at it very fast. I think it is a very good way to train.
The bike must have weighted ~22lbs.

For the recap :
A suitable yet heavy frame with race geometry.
A hard ratio in single speed. 52/16 is a track ratio AFAIK.
Parts : decent & quasi-decent.

Do you have such bikes ?

Reading your post made my 47 year old knees ache.

Yes, and they've been used for training for a long time. Lot's of guys train on fixed gear. Locally a couple of them will use flip/flop bikes, go like crazy fixed for 20 miles, then flip 'em and ride back for recovery. Pretty much shreds the legs for a day or so.

"Train heavy, race light" has been around for a long time; but it's given way in many cases to simply adding resistance. Lot's of good criterium riders train on 700x28's running lower pressure, or even a heavy wheelset, as they've found the frame not to me much of a factor. I know a guy who trains on a Cannondale touring bike with front and rear baskets, like a newspaper bike on a diet....He regularly trains at 21-22mph, and often borrows bikes to race. In team triathlons, he's the one you want...

I use a Raleigh Rapide set up as a single-speed with the FD/RD removed, small chainring gone, and bullhorn bars. The hardest thing is to resist the urge to shift.