The problems  aren't a deal breaker, veneer is readily available, you've already found most parts beiekn are repopped. 
The lack of  selection could be a bad wire not energizing the selection pins, or 50 yrs of gunk gumming up the works ie selection pins, until you can actually check it out,  it's difficult to trouble shoot.
The Wurlitzer group   onmn Yahoo is bout the friendliest  help you're going to find on the internet. I still read the postings at The Jukebox-Archives, and alt.collecting.juke-boxes, The jukebox list can members can be brutal to a newbie, Alt.collecting isn't as popular as it was once was, but all three are resourses to use. 
i've also  talked to Denny at victory Glass for many a suggestion, don't be afraid to ask  the parts shops for help. 
jukebox- list archives : 
http://webreports.netlojix.com/pipermail/jukebox-list/Alt.Collecting.Jukeboxes:  
http://groups.google.com/group/alt.collecting.juke-boxes/topics?hl=en