I'm qualified to answer. We're going to Cuba in Septermber.
We're doing BNE-LAX-JFK//JFK-CUN-HAV//HAV-CUN-DFW-SCL//SCL-AFO//AFO-SCL-EZE//EZE-SCL-AKL-BNE (PHEW!)
There's no issues with stamps in passports.
You CANNOT have the cuba leg on the same ticket as any ticket involving an american stop or airline.
So essentially, you need to get to either mexico city or cancun then get a SEPARATELY TICKETED CUN-HAV-CUN or MEX-HAV-MEX etc.
Whilst the comment about not having a Cuba leg on the same ticket as any ticket involving an American
stop may be true for the OW fares, (I don't know, hence the "may") I wouldn't go so far as saying it's not true for *any* ticket, generalised.
There are tickets around where U.S. stops are permitted where Cuba is involved on the same ticket, just can't use a U.S. carrier flight number anywhere on the same ticket. That would be financial gain from Cuba for a U.S. company - big no-no. Star Alliance RTW's are one such ticket available.
I'll agree with you 100% about the no issue of stamps in passports. For the others that have posted don't go through U.S. with Cuban stamps in your passport - absolute bollocks. In this day and age of E-ticketing, advance pax information from airlines and the sharing of electronic data from other countries and airlines, they know you've been there anyway, more often than not, so what's the point of not having a stamp?
Mexico and Canada in particular share a lot of information about air travellers with the U.S., for obvious reasons, and as they are the two logical jump points to get into Cuba, you do the math about your odds of the U.S. not knowing your tavel movements priot to the U.S. !!

Lying about it would cause you far more grief than going through all the troubles to not get one IMHO.
This is of course, for non-U.S. nationals - U.S. nationals having a Cuba stamp would be a bit of a worry.
The U.S. DHS has no issue with non-U.S. citizens visiting Cuba and then visiting the U.S. afterwards, however U.S.
Customs do have an issue if you attempt to bring anything from Cuba into the U.S. I've seen something as innocent as a "Hola from Havana" postcard confiscated at the Customs check. As you need to "enter" the U.S., even as a transit these days, you are subject to possible Customs checks.
Also don't lie on your arrival forms and omit Cuba if you've been there before visiting the U.S. That's another huge red flag for them and as mentioned before, they already know more often than not.
As to getting in and out, there are the more well known usual methods via Mexico and also little known options via Air Canada & Canada. AC actually flies into 5 Cuban ports from various cities in Canada, pending the time of year. Varadero used to be served more often than Havana (not sure if that's still the case) and was a good option to get in and out, given it's proximity to Havana and the fact the Havana flights are often sold out.
The Star Alliance RTW used to be a brilliant option as Austrian served HAV and VRA nonstop from VIE, but since they dropped that route any Star RTW now requires backtracking through Canada. Maybe when CO join Star (*if* they're permitted to join Star probably a better use of wording!) they will drag their close associate COPA into Star with them and that will open up the Star RTW again.