7/25/2014 Application Submitted online
7/28 Prints @ Val Verde County Sheriff's Office
7/29 CHL-100 and Fingerprint Receipt Submitted online
8/9 Plastic
I'm just a computer dude, trying to make sense of it...
Here's a thought. If you submit on paper, there are clerical steps involved that will take time. Things like data entry, and document scanning. Then there are messy desks, lunch hours,
breaks, desk clean ups, lost docs, Monday's "now-where-was-I" 
, where'd-I-put-that-file, computer problems, 
everything that happens in an office. All this BEFORE your app can go into review, and your background check is started. Submitting paperless will reduce delays related to ...well ... paper..... and the labor that is required to process paper. Paperless submission means you do your own data entry, your own scanning, and you'll make less mistakes, and have less typos. It means your SS and DL numbers don't get transposed by a dyslexic state employee - bless their heart... 
Consider the logistics of the labor involved. The crew processing the paperless applications is probably different than the crew opening envelopes, and entering your data. The paperless crew probably processes more apps in less time. It would not make sense to take the day's hard-mail and try to merge it with the pool of paperless submissions. Fair, yes, but not practical. In this situation, data entry and data processing are two entirely different tasks, with two different rates of completion. Paperless submissions probably jump into the "review" state much faster. They probably have less problems during review.
And one more thing .... mixed submissions. I'd bet mixed submissions are the slowest of all. Where some of an applicant's documentation is submitted paperless, and some of it is submitted hard copy.... That scenario would be the most time consuming to process, and it requires a lot of "inter-office communication" to match things up..... now your application is subjected to two lunch schedules, two break schedules, two messy desks.... two vacation schedules... an app could easily gain 6 weeks of processing time, even if the applicant was Jesus.....
Not tryin' tell you how it's done, just suggesting - if it were my office, I'd need a hard-copy crew to do the data entry from hard copy.
I'd need a "Match Maker" crew to take the data entered by the hard copy crew, and match it with online submissions - at that point, all elements of the application are finally paperless. Then it would get passed to my paperless crew, who has been sitting on incomplete online submissions, waiting for the other crews to feed them the documentation they need to go forward. Meanwhile, when a new app comes through, complete, in a nice neat paperless package, the paperless crew jumps on it, whisking it through in 10 days. Why wait?
That is my attempt at reverse engineering the wait time anomaly .... It would be interesting to look at the work-flow and see where the hangups are. We'd probably see applicants with scanners, submitting completely paperless, getting plastic much faster than people with envelopes and stamps.