After reading most of this thread and a few others about the Velocity Strategy.
I've finally wrapped my mind around this.
Does this strategy work? Yes, but here's why it works.
I'll take a common example that's been shown a few times:
You get a HELOC for $20k and take $10k out.
You put this initial $10k down on your primary mortgage. It goes directly towards your loan paying off $10k in principle.
You have $1k/mo in discretional income after paying all expenses. So it takes you 10 months to pay off this $10k. So you can repeat the process over and over again. You're effectively paying down $1k/mo in principle payments through the HELOC.
If you take that same $1k/mo that goes to paying off the $10k chunks and instead put it directly into your mortgage you achieve a better result. You don't pay the HELOC's higher interest rate
You can improve this pay-off result even further through bi-weekly payments of $500/mo instead of one time monthly payments of $1k.
As far as having cash available every month? You can still get a HELOC and only use it when you need it. You don't need to flip flop between HELOC to mortgage. You can pay the $1k/mo to your mortgage directly and use the HELOC when/if needed.