I'd agree that 6/14 would be rushing big time. You could cold crash the fermenter to get it to clear up but that would stop all yeat activity. On a beer that big, you really want to let it sit for like 3 weeks in the primary, cold crash for 3 days, then rack to keg and put it on the gas. Even then, it could use a good 2 weeks of cold conditioning. My philosophy on rushing beers for events goes like this.. 99% of the population already has it in their head the homebrew is sub par bath water. Why would you want to confirm that for them by rushing it?
The only two beers I can imagine being drinkable in 17 days is a wheat beer and a mild.
I'll get off the soapbox and tell you how I'd do it to get it ready by the 21st because I'm guess you'll serve it no matter what. Cold crash the primary to about 34F tonight and wait until Wednesday night to carefully rack to keg. Apply 30psi, pull the dump valve to purge oxygen out for 1 second, re-apply the 30psi. Rock the keg back and forth on your lap for 3 minutes. Put the keg in the cold and leave it at 30psi overnight. Thursday morning, drop the pressure down to 13-15psi, pull the pressure release for about a second and leave the keg alone until Saturday. See how you like the carbonation.