Shock length is the same for both early and late frames. 365mm between eye centres.
Rear wheel not lifting off the ground is not unusual, but if it's too heavily planted on the deck it'll be taking a lot of weight off the centre stand and the bike will be unstable on the stand.
If your Ikon shocks measure 365mm, then it could well be a problem with the stand. If the centre stand stops are worn, the stand will go too far over-centre causing the bike to sit too low. The stand pivot bolts could also be worn, or some bodge done with wrong diameter bolts. I've also seen bent centre stands.
Could also be the front forks. Marzocchi forks fitted to Laverda triples were a bit longer than the earlier Cerianis, so the centre stand was made a bit taller. Previous owners could have done all manner of odd things in the 36 years since it left the factory. It may have ended up with a a stand mis-matched to the forks.
It could be a combination of all of the above. My Jota had a bent and worn out centre stand with loose pivot bolts when I bought it, and the PO had also swapped the Ceriani forks for Marzocchi. The result was that the bike would teeter precariously on the centre stand.
Fitting a decent sidestand is also worth considering. Jim Bush used to make an excellent bracket to fit a Kawasaki sidestand but I think he's stopped doing it now. If you want to get one made by an engineering shop, the details are here
http://www.laverdaforum.com/forum/index.php?topic=87012.0.
Cheers,
Cam