Usually the Southeast Asian varieties-(like Nam Doc Mai)are polyembrionic; these are rather elongated fruits
Unfortunately,and as far as I know- the Indian derivatives (rounded in shape) like Tommy Atkins, dominate the markets and you would be wasting your time with them.
You may find -occasionally -the other varieties and try, but if so, you may need to use a warmed greenhouse for the winter and early spring.(??)
You would be better off-I think-by ordering some grafted trees of the small sized varieties and keep them in containers.

Atalafo Mangos, which are sold as either "Champagne" or "Honey" mangos are a polyembronic variety. You can normally find them at "Whole Foods" and similar stores in the spring.

mangos from Asian are Polyembryonic and often planted by seed in central America and Asia, thus many Asian varieties like Phillipine/Ataulfo have several varying seedling strains.

All Indian varieties are Monoembryonic thus only propagated through grafting.

Many Florida cultivars are crosses, from my experience the ones that are more Asian like generally do come true from seed like Rosigold, the Indian like varieties such as Carrie or Julie do not.

Its very easy to distinguish and Asian type from an Indian type

Indian mangos on left Asian on right
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Wow! Thanks for all the help. The only ones I've seen in this neck of the woods look like the Indian variety. I'll definitely watch carefully in the spring.

Have you tried looking in the Hispanic supermarkets? They also go by the name 'Manila' here in California.

i can mail you some in a flat rate box this season for $5, email me in about 6 months if you are still interested

Waldie, if you live around Seattle (or west coast WA) you will usually find no shortage of Altaufo, Champagne, or Manila mangoes in many Asian/Hispanic grocery stores and farmers markets. It is known by different names because of marketing ploys, but they are almost identical strains of the same type. They are polyembryonic and origins are traced back to the Indochinese/Philippine types of mangoes. While living in western WA, I found them at "Ranch 99" grocery store even during winter, as they were flown in from tropical regions of Mexico.

Polyembryonic seed 1/2 photo.

Second 1/2 of photo. List of polyembryonic mango seeds.