I expect that it was Free T3 that the doctor suggested could be a bit higher, not RT3. I say that because your Free T3 was a bit lower than last time, while FT4 increased slightly. I don't have an explanation for that other than possibly less conversion of T4 to T3. Although your ratio of FT3 to RT3 is not quite as good as in March, it would be considered adequate by many sources, so the option would be to wait until next round of tests in a month or so, or to add a bit of T3 to your med. I think that it all depends on how you are feeling at present.
Your ferritin is good, B12 only needs to be in the upper end of its range, and your D is close to the recommended level of 50.
So, all in all a pretty good report I would say.