I think this is a solid thought exercise, but I believe the assumption that the offering will be in the previously mentioned range of $4.25 to $6.25, no matter what the R/S ratio turns out to be, is incorrect.
At the current share price of 0.17 with a R/S of 100/1, the share price would be $17. Even if the share price took a 50% drop from that point (which I think would be very unlikely), you are looking at $8.50 per share.
It would be extreme malpractice to then offer shares in the $4.25 to $6.25 range. This range is not immutable. I believe the 9% dilution would be a reasonable ceiling for the dilution unless more money was raised. If the share price is higher, then the offering share price will be higher.