The wonderful Rose/Lychee flavor of Brewster is growing on me and even though it has a large seed, it is a very good water type Lychee and is a relatively good bearer.
Mauritius is a great bearer but as Rob stated, it has a subacid component which some people enjoy and others not so much. Sweetheart/fake Hak Ip is still a good Lychee with lots of chicken tongue seeds but according to reports on this forum, fruit set is hit or miss. I'm not sure why my friend Phase003 from GArdenWeb had such good fruit set on his small tree. He lived by the coast. My RIP tree flowered profusely but set very few fruit although it was still a young tree and partially shaded. They do produce huge fruit though, like 40+ grams if I remember correctly.
Bosworth 3 is a great Lychee. Some people don't like it because it has a weaker Rose/Lychee flavor but I love them. They are a smaller fruit but very sweet and has relatively small seeds with no tart component like what Mauritius has.
No Mai Tsze is the best Lychee I've ever eaten and I've eaten probably over 25+ varieties, many are no named varieties grown in China. NMT is likely to fruit only very rarely because it requires a certain growing condition and seems to like resting for several years before fruiting again. Even in China, it can be 2-3 years before it fruits after its last crop.
The single best Lychee for your needs will depend on your personal taste preferences and whether you put quality over production.
Simon