Can I use a phillips-head screw instead of slotted?

Using philips head screws is fine, but not traditional if they are someplace that shows.

As to where you can find them, on the West side of the pond the answer is virtually in every city. There are 3-4 well stocked hardware stores here in Portland, for instance. If it’s important to you, take a small magnet to be sure that they are solid brass and not just plated steel. Prices aren’t usually the best, but you can get hardware the same visit.

There are also companies specializing in fasteners in most industrial areas, either in person or by a web presence. They will usually sell by the hundred or by the gross. Try places like Rockler’s, Woodcrafter’s, Lee valley, McMaster Carr, Grainger, Fasteners inc, Bolts Direct…. most boat chandler its. this is standard industrial supply if you are trying to match hardware you have, talk to the maker. I bought in quantity befor I retired and specifying the fastener was a standard practice.
Just google brass screws and 68 million hits pop up. Again, if solid brass is what you are looking for, make sure that’s what the vendor is supplying, and not plated.
Just for grins, here is a place that will sell you oval head #5 screw for about a dime each. Just use the filters to get what you want.
https://www.fastenere.com/wood-screws?CatListingOffset=168&Offset=168&Per_Page=24&Sort_By=disp_order

Glad you found what you need.
If I had known you live here I would have mentioned about 6 places within a mile of woodcrafters.