How much pause time are we talking here, from turn-off to mux change, and from mux change to turn-on?
LEDs operated near their mux can noticeably deteriorate, and fast. It also depends on where they came from.
A client of mine didn't either because they are all MEs. So I convinced them to at least get a 40-60MHz DSO and they bought one from Instek for under $500 (new), because I told them I had the big Instek and was happy. They were amazed at what they could do with this thing. Non-EE stuff they never even thought about, like measuring reaction times of mechanical actuators, hydraulic stuff and whatnot. "How do we measure closure time on this thing here?" ... "Just use that scope with both channels on and a piezo" ... "Oh!"
We all had to get there, and most of us on our own. Don't give up, this looks like a good project to hone your skills and if you get it licked it can even make you some money.