POST requests from jQuery to PHP stuck if POST data exceeds several hundred characters

Have you checked your PHP configuration regarding your request length? There are several parameters controlling the allowed size of a request, I'll include the most important ones here (straight from php.ini with references).

; Maximum size of POST data that PHP will accept.
; Its value may be 0 to disable the limit. It is ignored if POST data reading
; is disabled through enable_post_data_reading.
; http://php.net/post-max-size
post_max_size = 10M

; How many GET/POST/COOKIE input variables may be accepted
max_input_vars = 1000

This one might need to be increased if you have a highly nested data structure in your post variables (rather unlikely)

; Maximum input variable nesting level
; http://php.net/max-input-nesting-level
max_input_nesting_level = 64

Hope this helps,

Kind regards and happy coding!