There were No4 MkII rifles stocked in walnut. Whether or not any of the Irish contract rifles were, probably has more to do with the price the Irish were willing to pay for the rifles. I presume walnut would have been a lot more expensive and may not have been available at the time of production.
Beech, is a European form of Birch. Not really, the leaves are similar though. It's good, straight grained and stable. It's not prone to swelling or warping and will take a stain well. Many of the WWII rifles with Beech stocks were actually stained to look like walnut and many were Birch as well. For some reason Beech is considered to be a second grade wood for rifles. I personally think it has more to do with snob appeal than function. Most of the laminated stocks of WWII were Beech and most of the laminated stocks that are so valued today are a combination of Beech and Ash.
The real deals of the year now are the Pakistani No4 MkII rifles. I finally decided to clean the dull finish from mine. It wasn't really a finish, thank goodness, just dirt and hardened cosmoline. The wood underneath is gorgeous. They shoot very well too.
As far as the Irish contract rifles commanding a higher price, the main reason for it is they were built at the pinnacle of No4 variant improvements as well as usually being in VG to New condition. The 50s production of Long Branch No4 MkI* rifles are starting to command top dollar as well. Especially the unissued ones. The same can be said for the Savage No4s and just about any No4 or No1 for that matter.
Really clean Lee Enfields always bring a premium and now that they are so much in demand, even more so. When I bought my 3 Irish contract rifles, one was in the wrap and one was fresh out of the wrap but fired. The other one was still in VG+ condition and they were priced accordingly. $125 NIW with matching accessories, few rounds fired, no accessories $350 (5 years later) and $200 for the VG+ rifle at the same time. I also purchased a 1950 Long Branch at the same time as the NIW. It was new, unfired other than the test rounds and full of grease. Thankfully the stock wasn't saturated. It was $90. The reason being was the seller felt it was worth less because it wasn't wrapped. To my knowledge, the Long Branch rifles never were wrapped and neither were the Savages.