"Vanguard says that since the distribution from my Roth to my brokerage account was in shares instead of cash or check, they can only serve this rollover only as a dollar amount and not by moving number of shares."
Well, that may be a limitation they choose to impose, but that's not a limitation required by the tax code.
As I said, the tax code explicitly prohibits to completing a rollover by substituting cash for the shares distributed in-kind. Doing so violates the same-property rule. Of course the IRS is not likely to catch such a violation without an audit, but it would still be a failed rollover and the cash deposit would actually be an ordinary Roth IRA contribution.
An actual permissible rollover is not taxable, even if done in-kind and the shares have dropped in value. You report the amount of the distribution that was rolled over based on the value of the property on the date of the distribution, not the value of the property on the date that the property was rolled over. In this case you would be reporting a rollover of $1,901.81 of distributed value (the entire value distributed).
