Go to this folder: Medieval II Total War\mods\SS6.3\data\world\maps\campaign\imperial_campaign
There you will find a file called descr_events. That's the file that makes all events happen at certain dates, which then unlocks new units / armors etc.
So let's say you want to start in 1370, 150 years later than the late campaign start. All the events which has a date from 1+ and up have to be changed by 150. If any of the values are lower than 150, change it to 1, just in case some triggers are required. Some events have two values, change both with -150 value. That's it, pretty easy but a bit time consuming. After that go to descr_strat and change starting year to 1370.
If you want any other starting date, just change all values with the difference between late era start (1220) and your preferred starting date.
Heads up, first round will be spammed by all the events that happens up to your starting date. That includes the great mortality if you start after 1348
For example; gothicarmor 200, 220, would then be gothicarmor 50, 70