Only way you can change is to just mix it up. I try to not sign via free agency RFA at all. I've played franchises as Tampa Bay, Detroit, Edmonton and Washington. The big thing to me is to not sign "big name" players. For example if Mike Green makes it to free agency, I just can't see him being in a Red Wings jersey or whatever. I've never traded FOR a big named player, maybe a 4th line guy or young prospects but never trade for big name dudes. To me the players are who make the team (duh!) so I find it most fun to try to leave guys like Patrick Kane, Crosby, Stamkos, to their respective teams as best I can.
The drafting part, well that's just all up to you. Why do you restart after 2-3 years? Most of the CHL players I draft aren't ready for the NHL until the 3rd year so you don't even get to get those kids into your system! I just got to year 3 with Detroit and Ryan Nugent Hopkins is a 79 overall in his first year of his 2-Way 3-Year deal!