Rufus, welcome to Cycle Chat. Good luck with the search.
Apologies in advance if you’ve already done the following but I think you are going to need a lot of patience and spread your search as far as possible.
Are you UK based? If so there is here and retrobike.co.uk where you can look.
http://hilarystone.com/rims700.html is also a good place to look.
Looking further afield subito.it is the main Italian 2nd hand website. And you can easily search Fiamme and legnano. The question will be whether the seller is willing to post to where you are.
On Facebook there are a number of groups that might be able to help some public some you have to sign up to. Search using Italian Vintage Seel bike steel is real etc throws up these and more.
https://m.facebook.com/groups/42851702426?group_view_referrer=search
https://m.facebook.com/groups/Itali...i-Cfj97M4lRU55EQRyKxi6nhBTkRbnT847pjgS7vs9Gx4.
Locally to you there may also be bike Jumbles or other enthusiast sales.
Most importantly can you post some photos of the restoration in,progress, it ou le be great to see a 53 Roma