may do you'll leave from kashgar riding/driving chinese plate veichles or are you coming from a third country?
as is this the case you should to manage the paperworks through a local agency, wich it require a lot of time, say 2/3 months...
is this what do you mean for delays or is about road conditions? i also think end of may could it be a little bit cold to ride up there.
i was, sorry, we were 7 bikes on last end of august riding on the reverse way from kyr to pak. get in xinjiang for a 6 days transit with an agency from kashgar. the road on both sides of the torugart is under reconstruction. they've make it wider, but still gravel at that time. they should be able to turn it into tarmac this year. hope it for you.