I was occasionally getting pain in that region a couple of years ago. Went to the doctor, didn't establish the cause but did at least rule out anything serious.
I eventually worked out that it was a combination of wearing a belt and the seating position in my car putting pressure on the area just above my genitals. I (mostly) stopped wearing a belt and haven't had any problems since.
I did London to Leuchars on the sleeper a couple of weeks ago, in a reclining seat. Found it comfortable, but only got about 4 or 5 hours sleep. Every time the train stopped I woke up, and it stopped a lot.
You might do better in a cabin, but if they end up splitting the train in half at 2 in the morning I doubt you'll sleep through it.
Oh, and if you're driving to Euston:
1) leave plenty of time, I nearly missed the train
2) book the car park in advance, it's a lot cheaper