Hi Rick,
Depends exactly what you are asking, and exactly what you mean by a 1978 sport-
If you want to return a bike to exactly as it left the factory then you need to know when it was actually made- many morini sat in dealers for a while before sold and in the UK in particular the importers I think tended to buy the remaining stock from the outgoing year, so uk registered bikes are often strictly speaking a bit older than their first registration suggests.
Once you know when it was made then you can make a bit of a guess at the likely paint scheme it was made with, and then once you know that you can focus on the specifics of exactly where pinstripes are, what colour etc- but as Steve says, no two were ever much the same, and there was definitely an element of using up stock on the shelf, so especially during transition years there can be quite a few variations on the theme, so there are no real hard and fast rules.
77/78 was a change year in which the electric start was introduced, so an easy check would be does your bike have an electric start (or evidence one was once fitted)
I *think* 78 was also the year forks went black so that can be a guide but obviously you can’t easily tell if painted parts have been stripped/repainted.
You can look at the date stamps on the wheels- they are in a circular boss on the rim in the format MM/YY. Again, only tells when the wheel was made, and doesn’t guarantee the bike left the factory wearing those wheels but it’s all bits of evidence to point at a model year.
Once you have best estimated the model year you are aiming for then have a look at as many pictures as you can of the type you are aiming for and replicate the one you like the look of best, in the colour you like best. There were variations from the factory and some look ‘right’ to one person’s eye but not another- it’s your bike so should be how you like it. Nobody in the morini world will criticise you for getting it ‘wrong’ (you’ll more likely get flak for trying to get it too ‘right’ as they weren’t all clones in the first place!!)
Regarding decals- paint and painted pinstripes all the way- about the only decal is on the forks/shocks.
The size and shape of the black block on the ‘77 varies quite a lot for example.
Page 194 and 195 in the Massimo Clarke book give a couple of photos as a useful comparison, or the below link is not a bad starter for 10, at least to see the general basic paint scheme variations by model year:
http://www.motomoriniclub.com/lemoto/350stradali.php
I’m sure owners would be happy to post pictures of their bikes if you let us know which model you are after info on.
Finally, if you PM me your frame number I can look up in the club records and help you determine production date.
Keep us updated, sounds like you are on an interesting journey.