But there are lots of other dialects that do strange things with verbs after "if." Larry gave one in his post: "If I be late, I would be in trouble." I understand the be, but the tenses are weird.

To my knowledge, which might be wrong, "I be running" in AAVE is frequentative, whereas "I running" has the progressive sense. So you would say "I be running after church [on] Sundays."