I really, really hope you can find a way to get yourself centered and calm before, throughout and after you talk with H.
The only additional thing I wonder if I should ask him first is if this latest development has changed his interest in reconciling or if that's what he still wants to work towards.
Nope. This is your anxiety coming out here and it comes across as pressure to H if you ask him about it. Your mindset is that you two are already on the path of reconciliation. Keep the focus on how to address the OW moving to H's company facility. This is just a new wrinkle and you two need to figure out a way to face it together.
Try to keep an open mind on what H says and/or brings up. Try to go with the discussion flow.