Hey Mike , here's how I look at it, in it's most basic form :
The HRM amps can be viewed as hot-rodded-marshalls. The non-HRM amps(124,183,102,etc) can be viewed as hot-rodded-fenders. HRMs have 2 tone stacks, and the non-HRMs have 1.
Now some folks, or most folks will say that for an HRM to do it's thing in OD mode, the first tone stack, after the 1st stage(which is the stack for clean mode, and the same location that the non-HRM amps have), must be lifted using the PAB function(a tone stack lift). If you look at the HRMs like this, you'll see that these amps resemble a 4 gain stage, plate driven Marshall type, as they posses a stack after the 4th gain stage.
The non-HRM amps can be looked at as a non-reverb Fender(stage,stack,stage) in clean mode, then 2 added gain stages after that, and of course without the HRM stack at the end.
So yes, 124 and 183 are non-HRM.
If you're looking for an HRM that's straight OD, there is a "minimalist" schematic, which has the 1st tonestack removed. I built one recently and tweaked it to my own tastes :
https://tubeamparchive.com/viewtopic.php?t=27241
There is also a Bluesmaster HRM :
https://tubeamparchive.com/viewtopic.php?t=12875
I think the Weber "Heather" is their SLO, and their "Halley" is indeed their HRM. So if you used the Halley platform, you could do HRM or non-HRM. Of course the usual pitfalls of layout and component selection may apply.
Check out the "2nd gen" and "3rd gen" threads in the Files section, too, for more non-HRMs. There are more schematics and layouts there.
But you'll just have to build them all and see what you like best
Good luck!!