I use that Stanton 500 pick up and a range of different custom made styli.
Bought it from a now out of business company called "78 Archival Supplies"
about 12 years ago, I guess. I still got all the old letters with
correspondence, all sheets and listings from them that also contains the
whole range of styli they had in stock at that time. According to styli for
playback of Edisons verticals, the sheets tells that the correct styli would
be the 3.7 T or 3.7 types. BUT; when I ask spesific for the correct styli to
buy I received a letter that tells:

" After consulting with an engineer at Rodgers & Hammerstein at Lincoln
Center in New York (may it be Mr. Tom Owen???..) we have sent on his
reccomendation the following for your vertical "hill and dale" discs:
a) 3.7 Edison Ball: this works better on Pathe's than Edison, so I have
labeled it 3.7 Pathe on the invoice. You can also, of course try it on
Diamond Discs.
b) 2.6T: This has been found to work well with with Diamond Discs and in
adition is a good alternate stylus for normal lateral recordings (so you get
two for the price of one!). In addition, this tylus is good for many rough
starts as well as well as some Vocalion and brusnwick recordings with
excessive noise. it doesn't work all the time, but when it does it is a
"miracle worker". Yours sincerely Ricjard D. Markel (januar 24.1995)."

So this is what I have got; BUT at a later time I found this at the pages of
a company called Esoteric Sound.

They offer a stylus called Rek-O-Kut D5130E, that is a 3,0 mil type. It
"This larger size is ideal for most 78 RPM records because it will play
above some of the groove wear, while the elliptical shape compensates for
the larger shape in the reproduction of highs."

BUT; most interesting, it tells to work correct on Edison Diamond Discs as
well! There is a letter they refer to as well that confirms this. Just click
on the link above and open the document dated from 1951.

Here are the spesifications for the Rek-O-Kut D-5130E from Esoteric Sound:

Compatible cartridges: All Stanton 500 series, 700 series
Tip material: Diamond
Tip shape: Elliptical
Stylus dimensions: 3 mil X 0.5 mil (75 microns X 13 microns)
Tracking force: 2 to 7 Grams
Recommended discs: All electrical, most acoustic 78s, Edison Diamond Discs,
some 16"
broadcast transcriptions

WELL; this is all I've got on this subject and the correspondence I have
kept in my files!

ANYWAY; myself I have used both this 3.0 and 2.6, but never the 3.7. 
Maybe I should???

Best regards
Jan Myren