How is partner supposed to express I was going to pass 3♠X if you now bid. Consequently pass in a flash and your partner will realize he has to bid here just like he would over 3♠X [i.e. HE MUST SAVE YOU FROM PASSING] This also prevents psyches in this situation.
Welcome to the human race. BTW BTDT (too many times, of course once is too many :) ) Just be glad you don't do this often or at least as often as the guys you are playing.
I would bite the dust with the ♣A. It is not from a clear tenace. I hate a singleton trump lead here and I hate the ♠A for fear that it will set up dummy's ♠s with a possible entry when declarer ruffs the OL.
J2NT if you want to find out if partner has ♣ shortage otherwise show your hand with 2♣ while the splinter has merit as some have noted this hand is too good for one. I would prefer 3♣ to be a jumpshift worthy suit which this is not.
for me, I would assume it is a splinter but you need to be cautious I have seen some PUPs use it as stronger than 2♠ (note there is no player quality in the PUP acronym) and they don't use PJS :)