I have been playing drums for 40 years now and yes there has been many a time when one had to change from brushes to sticks (and back!)
Well if I knew there was only going to be one change I sometimes used to put the brushes under my arms to support them there and grab the sticks from a holder that is mounted down on the high hat stand. They are great and enable you to grab the tops of the sticks easily.
Another option is to have a music stand very near your high hats set up so it is horizontal. You lay a towel on top of it and you can put quite a few things on it and they wont move around much.
You have got your timing wrong above. I beat is 60/110 which is 0.54 secs. I bar of 4/4 is only 2.18 seconds. That could be pushing it. 2 bars or just over 4 seconds is quite a long time and would enable one to put down one set of implements and gather up another and also putting the first set down OK.
Jazz ballads sometimes go from brushes to sticks but the change over is usually at a time when the drums don't have to be involved in things so much and the rest of the ensemble might be doing a turnaround with accents or something else. Another option is to stop the music completely into silence and bring it all back in at the same time with the drummer playing something with else.