I noticed you mentioned you did not have a permit, keep in mind the loop you are considering requires 2 permits. One for the MR and one for the MT. The MT is a lottery permit (but some are available still) and the MR is reserved 6 months in advance in most cases through www.recreation.gov. The MT permit does not allow you to take the MR and vica versa.

Just a heads up in case you did not know.