Special Assistance on arrival at Heathrow is patchy. The advice is to wait onboard until the rest of the passengers have disembarked, and then depending on what has been booked they come and get you or you walk out to meet someone on or near the airbridge. It can take a while, there's often one buggy for a few passengers and you're moving at the speed of the slowest. I think you might find they'd be escorted entirely airside on a transfer too, not sure about that. I would be inclined to meet them airside in Dublin and follow on with them on the same flight if you can, that way you get the maximum flexibility.

Dublin is a bit hairy for B2B - the security is rather variable with a lot of random secondaries. Having said that, most people I know who've tried it HBO have been fine but there's always the time it's not and probably this would be a bad one for that to happen on! You can often pick up FR or EI flights inexpensively for the outbound and have a bit of a buffer. If staying in Dublin I think there are premier Inns and so on which are a little less expensive than the airport hotels.

They'll be handed BPs in Dublin when they check in with "First" written on, so you may not be able to sustain the illusion for long. Good luck anyway.