Hi Robbie , I have listened to the sound files of Jack Conway's unknown
titles and can add the following.

Tune 644-2 is "Always Be Honey To Me" (Branen, Lange & Prival).

Tune 644-3 I am not sure of at the moment, but it sounds like an "Irish
Flavoured" song, perhaps of Chauncey Olcott.  The problem is there were
lots of these 'Irish' songs around 1914-1916 and many of them sound
much the same!

Tune 644-5, which you have identified as "Ruff Johnson's Harmony Band",
is _not_ that song -- I have three piano rolls of 'Ruff' (or spelled
sometimes 'Rufe') 'Johnson's Harmony Band'.  But, I recognized the tune
and after a bit of hunting it down, I can correctly identify the tune
as "In The Valley Of The Nile", written in 1915 by Richard A. Whiting.

It can be heard as the second tune in a medley played by the Victor
Military Band, on the Library of Congress 'National Jukebox' web site.
The record is entitled "Loading Up The Mandy Lee", Medley one-step,
recorded in 1916.  You can also hear "Ruff Johnson" on the same site!

Tune 1845-5 is from the musical play "Mercenary Mary"; the song is
"Honey, I'm In Love With You".  It can be heard on YouTube being played
by Paul Whiteman's Dance Orchestra on a Victor recording of 1925.

Best wishes for now,
Paul Baker
Gosport, England

 [ Good work, Paul!  I found these audio recordings as confirmation:
 [ 644-2  Always Be Honey To Me (1915, Arthur Lange, Jeff T. Branen)
 [   ref. http://www.loc.gov/jukebox/recordings/detail/id/4244 
 [ 644-5 In the Valley of the Nile (1915, Richard A. Whiting)
 [   ref. http://www.loc.gov/jukebox/recordings/detail/id/4519 
 [ -- Robbie