I finally got around to watching that BBC documentary you posted back-in-the-day, Nuke. I think the engine actually might be even more f-ing awesome if they used an annular aerospike nozzle for the exhaust.
As per helium... it is heavier than hydrogen, and thus less likely to escape its containment. Being as active a gas as it is, well, it will still do a lot of escaping. But it's also non-reactive. If your heat exchangers are as fragile as they are, and they're being used to channel mass amounts of air to be combusted... you probably do not want to use a highly active, reactive gas like hydrogen to pump through the exhangers. Granted, carrying a separate set of gas tanks is a bit lossy, but when it comes to mitigating disaster, the weight gain is really worth it.