jgauffin's answer is close, but I found that (with R# 2017) to reorder Properties I needed to click the 'XAML' option in the header of the File Layout dialog and change
<Entry DisplayName="Properties, Indexers">
<Entry.Match>
<Or>
<Kind Is="Property" />
<Kind Is="Indexer" />
</Or>
</Entry.Match>
</Entry>
to
<Entry DisplayName="Properties, Indexers">
<Entry.Match>
<Or>
<Kind Is="Property" />
<Kind Is="Indexer" />
</Or>
</Entry.Match>
<Entry.SortBy>
<Name />
</Entry.SortBy>
</Entry>
The 'Sort By' property was empty and read-only, which makes sense because it's only used for items with the same name (and all properties should be uniquely named)