What to Order if I Like H&H Anniversary Kake?

These would probably scratch the same itch...
McClelland Top Hat and Beacon or Beacon Extra, or Pebblecut

C&D Night Train

Captain Earle's Honor Blend

GL Pease Cairo (not like Anni Kake, but you'll probably like it for the same reasons)

Excellent suggestions by Cortez.
I would also recommend GL Pease's Haddo's Delight and Rattray's Marlin Flake. Anniversary Kake is among the richest, plummiest of VaPers, especially when aged. So you're going to be hard-pressed to match that unique flavor profile. But Marlin Flake will deliver some of that plum with some higher sweet notes. Haddo's will give you the kitchen sink of Perique flavor profiles, transforming from sweet, to stewed-fruity, to spicey as the bowl progresses.
[If you like the Cairo that Cortez suggested, and/or the Haddo's, you'll have your hands full with a huge variety of Va/Bur/Per hybrids. Two I would recommend in that zone are McConnell's Scottish Cake (one of my top favorites), HH Acadian Perique, and Peterson's Irish Oak. These are less overtly flavored than Cairo & Haddo's, but are delicious nonetheless.]
You'll love the Escudo you have on your order list, but it will present very differently from Anni Kake. Assuming you like the Escudo (who doesn't?), I would recommend GL Pease's Fillmore.

Maybe order more Anni Kake. I've just tried it, courtesy of a sample sent by a Forums member, and it is delightful. There are so many versions of Va/Per, but this one is done just right.

Old Gowrie

If you like Anni Kake, you may like H&H Virginia Spice.

I am a huge Anni Kake fan. And I have not found anything like it. I've tried other VaPer blends most are too strong on the perique. Order more Anni Kake!

Now smoking the last of my stash of James Fox Squire’s Mixture in a 2003 medium bent Ural meer with a lined and etched egg shaped bowl.

It's no kind of match, but if you like Anni Kake, you might also enjoy PS Luxury Navy Flake, or (I've heard) PS Luxury Bullseye Flake, both now on sale at PC, at $1.75 an ounce if you buy at least 4 ounces; you won't see that price again soon, I don't think.

Try McClellands Black Parrot. Sip it slowly.

I am glad to see you ordered more Anni Kake with your new selections. I have also taken a feel liking to it and throw in a tin when ever I order trying to build up a stock in the cellar. I definitely like trying new stuff, but don't see much of a reason to stray to far from a favorite.

I'm a little late to this bus, but I think your choice of GL Pease Haddos Delight was a good one. They aren't the same, but cousins and I enjoy them both.
And Kudos ordering more Anniversary Kake- its good fresh, and GREAT with some age. Stick some in a jar and forget about it for awhile. If you didn't know, in October Pipesandcigars.com has a buy 2 get one free sale on 8 oz H&H products- you can get 1.5 pounds of anni kake for under $40!
I did notice H&H is also producing a new blend called Viparati I think which is supposed to be a real grown up version of anniversary Kake.
Finally, if you have not tried Escudo, its the gold standard of VaPers and you simply must try it sometime.