The main problem with these spaces is that they're almost fully enclosed, so you have to cantilever the bike out in front of you as you wiggle it in and hook the rim on the hook.
Dangly bike space designers have no concept of the need to hang a recumbent bike, nor the constraints the owners have to deal with. Like their train operating companies, they would really rather all bicycles and their owners would just go away and never come back.
I bought my Lightning P-38 partly because I knew it would fit (for moderately large values of fit) in bike spaces, because of its relatively compact length. Kim's earlier thread about IEP has the dimensions, I think. My technique is to use the larger, left-hand bike space if I can, and I balance the bike on the front wheel somewhat to manoeuvre it backwards into the bike space. Hanging it up by the rear wheel is awkward, and I am one of those tall people. I also know from experience that my bike can't be hung by the front wheel.
CrossCountry staff run the full gamut from "Blitz spirit" to "Self-important jobsworth", so you can't rely on anything, but possession of a cycle reservation is likely to strengthen your case. Expect staff to disbelieve that the bike will fit until they see you do it, because to the untrained eye a recumbent is about three times longer than a DF bicycle (while also somehow being invisible).
This exactly matches my recent trip. I was only going from Edinburgh to Berwick-upon-Tweed onna CrossCountry Voyager, but I had to argue my case on the platform at Waverley that my bike would fit!
'Are you waiting for the next train? Where are you going to?'
'Yes, I'm on the next one, going to Berwick. I have my reservation here.'
'You know your bike won't fit.'
'It's a CrossCountry Voyager isn't it? It'll fit
1. I've done it many times before.'
'I've seen people two or three times before, and recumbent bikes are too long.'
'Well I hope to change your experience for the better. It'll fit, don't worry!' and so on. The train dispatcher never looked better than doubtful, and eventually he wandered off to try to annoy someone else.
Once in place, I tend to fit a light-duty ratchet strap around the bike to secure it against the side panel, preventing it from swaying about as much and bashing handlebar mounted stuff (chiefly bell/mirror). This wouldn't be necessary with tiller steering.
I carry
2 a thin bungee cord that I wrap around the nearest vertical handrail/pole and attach to the bike's frame somewhere around the steering mast. Otherwise my bike swings around like a mad thing, and clonks into the handrail or the wall of the hanging space.
1 'What the hell? Why won't it fit?' I said to myself while trying to hang the bike up by the front wheel, because it had been ages since I last had to do it.
2 Naturally, I forgot it when travelling to Berwick.