I like the difficulty of the position assignments, I don't want it to be too easy. My preference would be either to re-draw using only team past the NBA/ABA merger or make each season/team combo an option instead of doing separately. If you were worried about how difficult it would be to make that list, I think I could put one together in a couple of minutes using a spreadsheet I have. I definitely do not want to go by decade or doing whole franchise.
If you want to preserve the draws already made, I could go with your proposal to get rid of position designations, but it isn't my preference. It is just going to create situations where the entire team is made up of 95% guys from each owners 1-2 modern teams. I would abide if it was the preference though.