This is a very interesting problem.
I disagree with the use of any form of percent returns -- conventional or logarithmic -- simply because they are nonsensical for negative equity values (I am assuming this price series is from some sort of margined position?). You are forced to choose between the mathematically "correct" returns for those which are "correct" from the point of view of the account holder.
Consider the final two results: a negative equity balance of -7.30 followed by an improvement to a negative balance of -7.18. Conventionally, that's a -1.64% move (-7.18 / -7.30 - 1), even though of course we can see that the account balance is moving positively (in the account holder's favor).
Is it "right"? Sure, mathematically -7.18 is -1.64% from -7.30. But if you try to calculate any statistics off these returns, the winning and losing days will be reversed -- so it's not right from a practicality standpoint and will ruin your perception of the account's performance (like average return, trend, risk).
It is correct, however, if we consider that it is the return experienced by whomever is "in the money" with regard to this margin account at that time. When the account balance is positive, the account holder is (presumably) experiencing gains. When the balance is negative, the margin lender is experiencing gains. Percent returns calculated conventionally are a reflection of their respective positions times the sign of their cumulative profit.
Logarithmic returns suffer from exactly the same problem -- moving toward zero is always considered a "negative" return, disregarding the fact that there is a negative equity balance.
However, for the sake of answering part of your question, you can in fact calculate logarithmic returns for your negative price series, with the exception of the one point where it crosses zero. Note that log(x) - log(y) = log(x/y). Therefore, instead of differencing the log of two numbers, just take the logarithm of their ratio. The example I gave above becomes log(-7.18 / -7.30) = -1.65%, which is very close to the arithmetic result.
At the crossing point, this method will fail, and you may have to fall back on an arithmetic calculation (with all the caveats above).
The best way to do this is to use a margin balance or risk capital position. Add that to the price series to de-lever it and avoid negative balances. Then either method of calculating returns will work as normal.