Contact cement may be the easiest approach for this purpose.  I have not used it for veneer but I have used it to attach other thin materials to a plywood substrate and it is pretty easy to do though you also only get one shot at it.  Once it makes contact anywhere you pretty much have to go forward.  

One of the nice things about hammer veneering with hot hide glue is that it is completely reversible if you screw it up.  Heat and moisture will soften the glue and you can re-hammer it down and you can do it as many times as necessary.  You can even completely remove it and start over.  I simply wet the spot and place a wet rag over it and used an old cloths iron to reactivate the glue so that I could re-hammer.   I think the key to being successful on this panel would be to cut the veneer into narrower strips -- 4-6".  You just need to make sure that the edges are nice and straight.  If the veneer is thin enough you can use a utility knife and straight edge to get nice straight lines.  Just becareful that you don't let the knife follow the grain as you cut.    The length is also a concern but as long as the temperature is not too cool (you can warm the substrate with a heater before you apply if necessary), with narrower strips , I think that it would be doable based upon my experience.   

Of course you have to get a way to heat your glue and get or make a veneer hammer but you can use a crock pot and there are several examples around for making your own hammer.  I learned most of what I know about the technique from Shipwright's blogs on Lumberjocks, though they screwed up the blogs so badly during their conversion  that they may be follow now.  Not sure if he has also posted them here. 

This was my first hammer veneering project.  The veneer I bought was in 5 or 6" strips and as you can see were cut into relatively short pieces. The most challenging part was the interior ring.   I cannot imagine trying this with any other technique, especially as a first attempt.    Contact cement would have been really difficult on this project as would have other veneering techniques.  Hide glue actually made this pretty easy. 

--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.