From what i understand (just internet reading...i have 0 experience otherwise) it seems a large majority of the problem, now at least, is at the background check done by the FBI. I dont understand the hangup but I have a few theories.
One theory is that since we're stuck in the NFA association, the background check has to be more exhaustive and something similar to getting suitability clearance to work on a government project containing sensitive information which can take a couple weeks (side note...having said clearance does not help expedite the approval process). However, I would think they could gain some efficiencies there by either adding a flag in the FBI system for individuals that have cleared a check within the past, say 6 months, which could then be linked to the ATF system. This implementation would mean that as soon as the ATF examiner gets the form they could run a check against the FBI system, validate the individual was recently cleared, and boom...insta-approval. Alternatively, since the forms are now distributed digitally, they could link multiple forms based on name / social number. Then its one check and they'd all get cleared. However, as we here know, "efficiency" is not a word in the government vocabulary.
The eForms system, from what i have seen, is kind of cludgey. They are essentially running an imbedded PDF engine but the form remains the same. Those systems can be kind of buggey due in part to the amount of resources required for rendering + processing...as we've seen. It would have been a nicer / more reliable design if they'd updated the eForm submission to be more of a standard web form with traditional text fields, boxes, and radios like those digital firearm transfer forms at the big retailers. Plus, it probably would have been less overhead from a development perspective to have gone that route. I'm arm chair quarterbacking and making a lot of assumptions about how their backend systems work though.
The current eForms implementation does address one of the previous lags in the process which was the literal mailing of forms between the agencies. I understand the previous process as; the ATF would get the form, it'd sit until an examiner was assigned, reviewed, sit until a batch worthy enough was stacked, batch mailed to the FBI, sit until an FBI investigator was assigned, checked, validated, then mailed back, sit until the examiner picked it up again, reviewed, approved, stamp assigned, mailed. Each one of those "sit and waits" was probably 1-2 months.
Anyway, I think the eForms system is a decent start to resolving a broken system. I think / hope we'll continue to see the eForms submissions be ~2x faster than the paper forms as evident in the timelines (200 days vs 400 days). A few additional changes in the interaction between the agencies would make it better and expedite the process though.
....or they could just remove suppressors from the NFA act since they dont really belong there and are, IMO, safety items similar in nature to earplugs...but they're scary and according to the movies will make firearms as quiet as rubber band slapping your wrist ¯\_(ツ)_/¯
They also generate tax revenue that can be erroneously used for things that it shouldnt be...like subsidizing student loan debt or padding a politicians wallet.