I'm wondering if anyone here has experience playing SR3 or SR4 up into the time frame of later editions. Are the events and changes doable with the older systems?

As an SR4 GM, I cherry-pick those events that make sense. For instance, I disregard that whole CFD nonsense in SR5 completely. FastJack is still running JackPoint.

Uhhh, this is hard...
SR3 was always the gameplay with a bit of flavour, but they did manage a good chunk of decent lore in SR4.

Honestly, I'm torn on this.
-Tir

Ask me in about 20 years....
Our game has been running for 6 years now, but we've only advanced the IC date from 1/12/59 to 20/3/61....It might speed up a little now the team are well geared, but I'm not counting on it.

SR3 hermetic mages and shamans are notably less potent than their SR4/5/6 brethren, because of the changes to drain and spirits. But if anything, using SR3 likely make SR4/5/6 stories more in line with the authors' intent, as the setting never really caught up on how lobbing materialized spirits at people from the safety astral plane should have entirely replaced police and military, firearms and missiles.

Changes in the Matrix actually don't affect the setting that much if you include SR3 [i]Matrix[i] rules for cellular connection, because from a data-centric point of view, there's no difference between hacking an objet through its wireless connection and hacking an object through a backbone access to the mainframe it is connected to. The biggest difference is the ability to deck/hack while walking in AR mode.