The preamble: Al alloys such as 6061 are tempered by first by heating to put all of the alloying elements, (Mn, Si, etc.) into solid solution, then quenching to approx. room temp. The alloy elements won’t do anything on their own for a few millennia or more; however if heat is applied, the elements will ‘precipitate’ into submicroscopic clumps that strengthen. So depending on the Time-Temp recipe you’ll get the various tempers designated as -T4, -T6, T7, etc. each having ad/disvantages. T6 is about optimum for strength. 375F for a couple hours could be ‘overaging’ like maybe into T7. You are doing something, so the descriptor of 'nonsense’ for this operation may not be totally accurate. (BTW T7 will be less strong, more ductile, I think, and better for corrosion resistance.)
Finally to answer your question - I think you should start at the beginning and get those elements all into solution, then quench or air cool the part. I may be wrong but that should be -T0. For sure, get a copy of the ASM Heat Treater’s Guide. The C2H2 treatment won't work - the part is too thick. Lastly for machinability, T6 should have very good chip formation, so reconsider annealing.