How do you bond clear acrylic to wood?
Consider a clear-drying epoxy. Note that not all epoxies are equal. In a general sense they can bond different materials together with ease.

Here is an earlier epoxy advertisement where they glued a car to a billboard with an epoxy resin. 




  1983 a visual stunt presentation was set up to show the strength of Araldite by gluing a yellow Ford Cortina to a billboard on Cromwell Road, London, with the tagline "It also sticks handles to teapots".


You can usually get 2 part epoxies in a dual syringe form and they are very economical. Depending how often you do this you might want to try a smaller one first as the shelf life of the product varies once used. 


  Cheap and quick curing options would be great but I understand you can't have the best of them all.


Only part about this that does not meet your requirements is that they have a longer curing time then something like a craft glue. Setting inside an hour but fully curing over several days is needed in some cases. 

The resin and hardener are kept separately as liquids, hence the dual syringe. In larger applications they would be two separate containers. I would suggest not applying directly to your project from the syringe but onto a disposable piece of cardboard or similar. That way you can manually mix the liquids together (usually 1:1 ratio) to ensure an effective reaction. Then use an applicator (craft sticks) to apply to the project.

You are going to want to clamp this down with decent pressure. There would be the issue of seepage while setting you need to be aware of. Depending on how intricate your cuts are the solution will come out of the wood acrylic sandwich. You want to try and wipe that off before  it sets. Epoxy resins dry really hard so if you have to cut part of it off it will no longer show clear on the cut. You can polish the edges once it cures with extra fine sand paper and / or a polishing compound.



A long term issue is that set epoxies can yellow over time because of UV radiation. That is likely a moot point as you are making a key chain.