The sort of "fast erasure" laptop you are dreaming about will probably not be either easier or harder to track down, than any commercially available "off the shelf" model you might buy at a computer dealer.
Consider the fact that most of the "volatility" of the laptop's data - the fact that it has no hard disk, that its RAM loses its content when the power goes off - makes no difference at all until *after* somebody has tracked you down and seized the laptop for inspection. At that point, they may be less able to find evidence that it was you who was posting hateful gibberish in a chat room... but they'll already have found you and will know who you are!
As to using phased-array antenna on your laptop - that might make it slightly harder for people to locate you by radio direction finding, if they're starting out at random locations. The same would be true of any directional antenna on your laptop. However, if they start RDF'ing for you from a location near the access point, having a directional or phased antenna on your laptop won't help a bit, since your antenna will be "beaming" its strongest signal right towards the access point. The same problem exists with using a maser (a highly impractical idea, by the way - they're big and clunky, and somebody would probably ask what you're doing pointing something that looks like a bazooka and has liquid-helium tanks at a coffee shop!)
How can they find which access point you're using? Pretty easy! In the situation you're thinking of (coffee shops), your postings will appear to originate from an IP address which belongs to the coffee shop itself. Either the coffee shop will have a range of routable IP addresses, one of which is temporarily assigned to your laptop (uncommon) or they'll have a single IP address, and your laptop's temporary "private network" address will be translated to theirs by their router.
In either case, your postings can be traced to the coffee shop. If you use a bunch of different coffee shops, you'll be revealing additional information about your location and habits. If somebody really wants to locate you, they can... every time you start posting, the access point's location can be determined. Post a few times from a few different locations, and somebody can correlate those times, and start looking at security-camera footage to see which individuals were near those locations at those times.
If you annoy people enough, they'll be able to find you.