Basically this, yes.
This statement at least resolves my problem with considering kaioken x4 in the scaling chain since it at least establishes that Goku in kk x4 should be a bit weaker than third form Freeza.
As for the kaioken x10 thing. I'd like to see the source for the translation you used in the OP, as I can't just take your word for it when every other English translation I have read makes it sound like Goku was just super pumped up and hyped after completing the training and experiencing the normal gravity where he felt weightless and strong. While I am not saying it has to be dead wrong or makes no sense, I am not too big on the reliability of the statement delivered
in this sense, and would not include it to keep the scaling conservative and to the hard facts with no assumptions. (I have also asked my friend for the translation btw.)