Well ASP just launched to the public a few weeks ago (everybody else had preordered between 5 months and a year ago during the fundraising campaigns). The goal of ASP is to only sell what parts are in stock (and thus have a quick turnaround) as opposed to on the main site where you order what you want and then wait not only your turn (SF churns out an insane number of sabers a week) but if the parts aren't in stock. The main site also has electronic options that ASP doesn't offer currently.
At the moment ASP is still being sold through IndieGoGo until the website for it is ready. And the turnaround has been fairly quick for those who have ordered through there since the public opening.
ASP sabers arrive with the hilt assembled but the electronics and timing shims separate.
There are hilt parts that have wrap options in ASP (on the body pieces, not pommels). Check out
saberparts.com for all available parts.
Be aware though, that Champion ASP electronics currently do not have a recharge port (like main site Champions do) but a removable battery (which I have heard cosplayers prefer since they can swap the battery on the fly). The Sabercore 2.0 boards don't have a deep sleep mode, so without a kill key (which you'd have with a recharge port) the board will still draw power even in standby, so you'll have to remove the battery when not in use for long periods of time otherwise it will drain in a couple days.
The main site wait time might be quickening up now that the Kickstarter and pre launch IndieGoGo preorders are out, but at best you'll be cutting it close and most likely just miss your convention.
Another option is SF's Etsy store, where the goal is also super quick turnarounds with in stock hilts and very limited customization options. There currently isn't a Katana as one of the options (so that doesn't help you now), but you might find something else you'll like.
For your needs (quick and customized), ASP might be the way to go.