So did you get any further, krikor?
Just wanted to point out, I think the defining character of VHS audio must be down to that 'Depth-Multiplexing' technique it uses (see Wiki quote in first post). I suspect that due to the way it's done, storing two signals at the same tape surface position, that what we hear is being contaminated in some non-obvious (but pleasing) way. At the end of the day they're still storing an analogue audio signal to tape, so I think it's really the Depth-Multiplexing part that makes VHS audio have a different characteristic to that of standard tape recording techniques.
So what I'm getting at is, I doubt ageing and glitches would get you that VHS audio characteristic. I do think tape recordings sound better after they've aged, so there is something of merit in the ageing process of a tape recording, but it's not what gives VHS audio it's unique characteristic.
Although I wouldn't know how to do all of this, I'm thinking that taking the audio signal, processing it with an appropriate form of distortion or 'drive', and then mixing a slightly offset copy of it with the original signal, might reasonably replicate the process where, with VHS, it gets recorded, erased, and re-recorded to the same part of the tape surface. What would need to happen to it in a modulation sense, I'm not entirely sure (perhaps an ultra-high frequncy amlplitude modulation to the cloned signal), but once I get a better understanding of some of the objects I'd definitely be exploring routes like that.