I used them in New Zealand last year in my 284 with Lapua brass, and borrowed a RCBS hand primer from another shooter to seat the primers. The lot that I used last year seated below flush without too much effort, but still had to use more force than a BR2 or some RWS primers he had. I would not imagine that they are getting different speced primers than we are getting in the US. I know one shooter that was struggling to get them below flush for his prcw that used Lapua 6.5 PRC brass necked up.
My CPS seats them fine for my prcw and 284 brass, and gives me very consistent sd/es numbers. The lot of WRE primers I used last year in NZ gave me an sd of 3 for 5 shot groups, so they work well.
Cheers
Now that I've gotten ahold of some White River LRP's (Magnums, since that's all that I could find), I've disassembled a couple and taken measurements and compared them to CCI 450's I have. It's quite an eye opener and, in my mind, explains a lot of the issue you're having with seating them.
For the most part the WRP's had pretty consistent diameters (almost as consistent as CCI's 450 at .2110"). I only measured 20, but that should be enough to get a good idea what what they're all like. Primer overall height ranged from .1325" to .136" (average being at .1344"). The two I disassembled had a cup height of .120" and .123". The primer weights ranged from 5.64 gr to 5.74 gr with an average of 5.704 gr. The WRP's weighed .484 gr on average more than the CCI's, which suggested heavier components. The two WRP cups measured .0175" thick compared to CCI's .017" thick (the best measurements I could get measuring multiple times). The 2 WRP foils both measured .012" thick. When looking very close at the anvils with magnification, the WRP's looked visibly thicker than the CCI's. Since I didn't have a way to measure the anvil thickness, I weighed them and sure enough, the WRP's were substantially heavier by .24 gr.
Like I previously posted, I took one of my ADG 6.5 PRC cases and seated one of these WRP's using my 21's Century hand seater that is set with a hard stop, which gave me .004" below flush with my Fed 210's. Well, the WRP didn't seat quite as smooth as there was notable resistance as it got to the hard stop. Upon measuring the seating, the WRP was barely below flush. Almost at flush, being just .0005 below flush using my Accuracy One primer gauge. I put the case back into the seater and squeezed to the hard stop a couple more times and the measurement didn't change. I decided to try one more and it only seated exactly flush. Then I thought, I'll adjust my hard stop that should normally give me an additional .004 of seating. I could feel a lot of unusual resistance as I squeezed to that hard stop. The two cases ended up with .0035 below flush.
Given the numbers I'm looking at, I'd say the overall height of the WRP's and the very thick anvil (and the foil too) makes it rather hard to seat them, where that thick anvil tends to resists being squeezed, especially into a someone's shallow primer pockets. Some of the variations making it particularly so. I think these WR LRP's are best suited for primer pockets that are at ~ .130" (like you might find with Peterson brass

, or trim pockets .004" deeper, which really shouldn't be any kind of big deal, especially if there's a thick web).
