The rules say you're allowed in.

Therefore your best course of action is to have a copy of those rules on your phone/iPad, ready to show the agent. Also, I would be minded not to take the escalator up to the lounge, where an agent is stationed at the bottom to do a quick eligibility check, but take the lift up instead, then speak to an agent at the desk. I think they'd be more likely to discuss access with you, and possibly be more knowledgeable about the rules (having access to a PC will help them in that sense). Over and above someone at the foot of an escalator armed only with a BP scanner and will not want to engage in a debate about it.

I do hope you get access. The lounge is lovely.

The lift is to the right of the escalator as you approach it.