According to Flightradar24, NAS currently has connections with airports in the following countries:
- USA - requires visa
- Canada - requires transit visa
- Cuba (Havana and Holguin) - the most flexible TWOV
- Jamaica - TWOV requires you to remain airside
- Haiti - TWOV requires you to remain airside
- Turks and Caicos - TWOV requires you to remain airside
- Panama - TWOV requires you to remain airside
All the TWOV which require you to remain airside are only applicable if you have both flights on the same ticket, which seems to be very unlikely.
Holguin only has flights to Havana and Cancun. We've seen previously that you probably can't TWOV in Cancun.
Havana has flights to:
- Port of Spain, Trinidad and Tobago - flexible TWOV
- Mexico City (not at the moment)
- Cancun (see above)
- Nicaragua - visa required
- Panama - see above
- Colombia - TWOV requires you to remain airside
- Venezuela - TWOV requires you to remain airside
- Argentina - TWOV requires you to remain airside (exceptions can be made but require the airline to escort your and be responsible for you, forget about it)
- United States - See above
- Spain, Italy, France, Switzerland - visa required
- Dominican Republic - TWOV requires you to remain airside
Port of Spain has flights from (other than the above):
- Curaçao - Flexible TWOV
- Guyana - TWOV requires you to remain airside
- Suriname - TWOV requires you to remain airside
- Sint Marten - ?
- Antigua and Barbuda - TWOV requires you to remain airside
- Barbados - TWOV requires you to remain airside
- A few other islands with no interesting connections
Other than the above, Curaçao has connections to:
- The Netherlands - visa required
So, no, there don't seem to be any easier options, at least at this time (there may be more options in normal "post-COVID" times).
Note however, that even for the very very few countries which allow flexible TWOV (like Russia and Cuba in your itinerary), I'm not sure any airline is going to let you board a flight to a destination where you're not allowed to enter, if you don't have an onward flight on the same ticket. To them, your final destination is the one on their ticket, and you need to be able to enter that destination. Since all those flights are on different tickets and different airlines, I would be very surprised if you ever got to your final destination.
I think the best option for you is probably to get a transit visa (probably several, actually) which would give you more options regarding routing.
If you have the means to travel to the Bahamas, it shouldn't be difficult to get a transit visa for many of the alternatives.
NB: I hope you're not trying to go there on holiday. Travelling for leisure at this time is a very, very bad idea.