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OK, given your tight timeline, here is what is most actionable:

1. Take the 2D pattern you've provided via *.ai file and create 3D printed letters using extrusion (FDM/FFF) with tabs for placement and alignment.  
2. Instead of the laser cut acrylic (at least at this time), I'd offer that we 3D print a large plate as a stop gap method as this is what we have immediate control over.  We can separate that part as a unique order and see if any of our laser cutters in our network will take the job.  Just harder to guarantee on short notice.
3. The "tabs", did you have any wiggle room to change those?  Or were those defined by your client?  Our recommendation would be to make those distinct, separate pieces of your letters, thereby allowing them to be inserted after the larger letters are printed.  Those, upon first glance, just seem to 1, position the letters on a platform and 2, keep them aligned.  The K and the A are also over constrained which if not toleranced correctly, will bind or possibly fail to insert after painting (as painting creates a thickness). 
4. I'd assume for base color, white or close to white would be beneficial?  We want to help you execute quickly and we regularly stock white PLA. 
5. Lastly, will your client be happy with "something" by Monday and if you deliver, would that buy you some time to upgrade your project with them?  Like, if we do a 3D printed base, you could swap out for acrylic at a later date?