You have my sympathy too, as our neighbours are having an (odd IMHO) extension built and it is upsetting Blip a lot. She too is reluctant to go outside and, as she won't use her indoor litter tray, this makes life difficult. I've taken to walking out into the garden with her to reassure her; this works but, as advice, it might not be of any use to you. I don't try and touch her - I just wander into the garden as if I wanted to be there. Could you do this during the workman's breaks etc?
I do think Feliway helps and just being as generally reassuring as you can, but I'm sure you're doing that already.