Sunshine Blue blueberry is perfect for your needs. Bears heavily, delicious, medium size fruit and is self fertile. Works well in mixed shrub borders or in large pots.

Would it be possible for me to just use a rabbiteye variety and keep it pruned to no taller than 3-4 feet?

Possible but in order to keep it short you likely would be pruning off blooms for the next year.

Use the word "compact" to search for cultivars. Monrovia seems to be growing at least two these days; Bountiful Blue and Peach Sorbet.

There is a website called patio blueberries but it is in Oregon.

Here is a link that might be useful: Peach sorbet