Yep, much better to use a desktop or laptop computer to interact with this site when it involves uploading. Your x-o pics look typical and fully original for this vintage of Rectilinears, and it looks like you've been able to successfully remove the plastic crossover panels from the cabinet boxes. All of those original electrolytic caps require replacement. The Rect-III was built with a few iterations over the years, and the only thing that jumps out at me is I'm more used to seeing a 2uF or 2.2uF cap on the small cone tweeters, and a 90uF cap for the Phillips midrange. I think I've seen versions with the 60 cap but have never seen a 5 cap before.
Generally speaking, film caps (polypropylene, polyester, etc.) tend to be much larger in size than same value electrolytic caps, and somewhat more costly, too. The smaller value replacement cap could easily become a film cap, but the high value (60uF) for the midrange cap would become surprisingly dimensionally large and rather costly if you used a film cap here. Probably, I would use good quality electrolytic caps here, and it may require combining additive values to reach something close to 60uF.
If you could share your schematic, that would be of interest - - there are a few schematics for this model floating around, but they seem to vary in configuration or stated values.