Just keep workin' it, you may be able to get it to move a bit by prying carefully w/a padded screwdriver (coupla layers of masking tape) by removing the air filter and going in through the inlet side. Pull gently on the cable while yer doing this - but careful, that lil nubbin on the end of the cable isn't all that rugged. Wiggling gently & time works far better with less damage than brute force.
A warning tho - the slide & pin may be damaged now and/or as a result of attempting to pry it out, while it may not be too bad and functional/fixable - don't sweat it too much, carbs are cheap and yours may have been flawed anyway if it simply wasn't assembled wrong.
Post pics of any damage/marring when you do get it apart... prolly wont be to bad but it'll be handy to see
You've prolly figured this out - but it'd be far easier to have the carb off the bike to do this
hmm... you mentioned previously that you could twist the throttle, ya might wanna check both the cable ends and the twist grip's plastic channel where the cable rests - you may have damage to those components as a result of the stuck slide. The plastic throttle in particular is suspect - I accidentally disemboweled one, pulling the cable end right through it simply by twistin' the throttle a touch too enthusiastically