The #1 issue why 2001 and early 2002 models will not e-start is that they had too much internal drag in the engine. In late 2002 the transmission was modified with a different tooth profile to lessen the drag. The following parts were changed: Counter Balancer, Balance Drive Shaft, Drive Gears on the Balancer Drive Shaft and the outer clutch basket. So if you are serious about getting your 01 – early 02 to e-start replace the above mentioned tranny parts with late 02-03 items. Probably 04-08 parts would work as well but I am not sure.
If you have a late 02 or 03 then a more powerful starter would be a good idea as the Autodecompression Device does not bleed off enough compression during e-starting. Using the 04-08 Cam and Autodecompression device Takes care of this issue. In 05 the 650’s received a larger starter motor than the 450’s.
2001 and early 2002 models had a solid starter “Reduction Gear” aka in late 02 as the “Torque Limiter”. This would cause damage to the starter motor and clutch basket if a backfire occurred during e-starting. These Reduction Gears were replaced with Torque Limiters under warranty. The gears should slip if 9-15 Nm of torque is applied. Make sure you have the Torque Limiter installed before attempting to e-start. In your post you stated that you shimmed the “Starter Gear” so it seems that you are probably good here as that is the way to fix a Torque Limiter.
Husaberg used to sell a thicker head gasket to help lower the compression. The 470’s seem to have a ton of compression. On my 2001 470 I have installed the Torque Limiter (under warranty), an 05 650 Starter Motor and bracket, thick Head Gasket and YTZ7S Battery. It will turn the motor over a few times before it runs the battery down or the sprag (or Torque Limiter) will slip. So lowering the compression a smidge and using a larger starter helped a tiny bit. A Husaberg factory mechanic told someone on this site to use 2 12V batteries connected in series to send 24 volts to the starter. This was before the engineers had addressed the starting problem.
A few have been able to get an 01, early 02 to e-start without changing the transmission gears by using: YTZ7S battery or equivalent, Larger starter, 04-08 Cam and Autodecompression Device and Dual Valves Springs (softer springs = less engine drag). I think that the battery would still run down fairly quickly even if it will spin fast enough to start.
The SEM ignition is yet another problem of sorts. I think that the engine needs to spin about 300 RPM before it will create a spark. So a very slow cranking motor will not cut it.
A 2001 or early 2002 will probably never e-start as good as a 04-08 model. If you don’t change the internal gears it will always be iffy. Sometimes though taking imperfection and trying to make it perfect or at least as good as possible can be a fun challenge.