Ben Lomond would be very tough on CX bike. Quite a lot of 7 stanes woulbe doable if you walk or run the odd bit.

7 stanes can be great on a cx bike – Mabie and Ae for definite, v smooth. Dalbeattie also a goer – a lot of fireroad, flatt-ish, but the singletrack is a bit rougher.
Glentress black up, red down is a great cx ride, although for 3 peaks training you could belt down deliverance in the drops to put some hairs on your chest.
Innerleithen is a great climb all the way up, but you’d be mincing down on a cross bike, and prob walking plora craig.

K’tree I’ve not done on the crosser – might be good. It’s quite stretched out and undulating, no big climbs, so you’d eat the miles. There are a lot of wee nadgery bits here and there, though, so I’d expect to walk some sections.
Don’t know if it would explicitly help train for the 3 peaks (never done it), but in terms of riding your cx bike where you might not normally then it sounds a good idea.

It would be good running downhill with a bike practice that’s for sure. I’m not sure there would be many opportunities to mount the bike, bar maybe 300m about half way down.

Has the OP thought about Conic Hill behind Balamaha? Starting from Drymen and follow the WHW up and over. It’s around 300m ascent and would be mix of ride / run. The downhill into Balamaha is steep but you should be able to have a bash it sections of it on the cross bike. Follow the road back to Drymen.

It’s much smoother being mainly grass.

If you want to train for the three peaks take your cross bike fell walking.
In my limited 2 year experience (4h40 and 4h01):

The road sections are for eating/drinking/recovering – find a group work with it and keep your speed up but no heroics.

You will walk up the climbs (not run) so get used to it. I find these the tough bits.

The downs are about damage limitation. Always see a few people flying down stuff then the inevitable bang as they hit something and crash or pinch flat.

There are plenty of bits that are reasonable to ride and you do take a beating but I’ve never really seen those as the bits where serious ground can be made.

Most of GT would be fine, i’d guess it is all rideable if you are good enough (I’d probably rule myself out of that one).

I rode Newcastleton Red and Black on my CX. They were fine.

Getting comfortable on harder trails is good practice but you’ll probably be ok if you are used to the bike and a half decent mtber.

It’s not the technicality of the black at GT it’s the rough surface that is the issue on a crosser for me.