*ahem* Well... Sorry for the bit of a 'Grave Dig' / Necropost, but.. Yes - Mags can Certainly be 're-tooled' (though, Newspaper / kraft paper, etc are Best - less ink / chems to floc-out, later) .. ie:
No need for those Official "Log Makers" (..that bend all up / usually aren't worth a dang in the end..), just a couple 5 Gal buckets, a 'drywall-mud mixer impeller' (I chose to replace the short-shaft with some nice, long threaded-rod and a bit of hardware.. saves the 'back'..) and Some sort of 'Press', to squeegee-out the majority of the water, from the slurry, ie:
So, first, you'll drill a Bajunchâ„¢ of holes in One bucket (...which can serve Many other purposes on the Homestead, anyway...) and you don't want them Too fine (otherwise, water-drainage is weak / takes f o r e v e r ..) but not Too
large, either, so'z you don't lose Lots of yer paper slurry, whence pressed. Nest the 'holey' bucket inside the Solid one, fill with water to maybe 3" below the top, and tear-up / shred Newspaper, kraft paper,
non-glossy (See *note below..) Magazines, etc into the water bath, and 'dunk' until you've got a nice thick 'stew' of papery-sludge..
*Note on any 'ink toxin' comments: IMHExperience doing this, I'd say the 'reason' to try and mostly use Uncoated / Non-Glossy paper for this, Isn't so much about 'ink-emollients' (most of any 'VOC's will have long evap'd, etc, and the Rest of anything 'yukky' / oily, will - pretty-much - end up getting washed out of the papers into this Bath, and discarded.
Where to Appropriately discard that 'grey water' is Up to You / research for
Your AO. Wouldn't recommend drinking and/or watering yer garden with it, but..
Point being: Most of that printing-skak will end-up Not in your 'logs'.. Do take care to Not put in, say, 'glassine-Window envelopes' (for obvious reasons..) It's more for the sake of 'expediency for drying time'.. Actual newsprint / kraft / bond-paper will dry
Much faster than the super-coated / varnished stuff..
BTW, this is a Great way to dispose of any 'sensitive documents' (ie: old financial docs / receipts w/ SS#s / CC#s, etc, etc.. Anything you might be inclined to shred / burn (vs the Obvious No-No of simply 'tossing'..) since whatever is on those papers Will be pretty much
eviscerated (...and later, burned, anyway..) so.. Pretty-doggone 'secure' way to get rid of such.
Anyhoo, so, once yer paper is all torn-up / soaked well, turn it into 'Oatmeal' with yer impeller, via cordless-drill (I find having the ability to Reverse-blend it is helpful..) till you've got a nice 'slurry'.. Don't want it Too thin, or Too thick (where it's Not able to 'churn' into itself..)
Then, sack out the 'holey' bucket, and let drain into the solid (I find using 3-4 of those 'bamboo garden stakes' make the perfect 'temp grate' to set the drain-bucket on, since they're nice and thin / keep the drainage going where you want it, below, yet sturdy...)
Once that's pretty-well done drip-drying (..Which is a Great time to sit in your rocker on the porch / enjoy a nice cold Tea / Beer / Wine / Whatever, and think about all you're Thankful for.

Then get your 'press' - which Can be Wood, say a 2" x 12", cut into a diameter to fit
Just-inside the bucket dia., But we chose to 'repurpose' a 3" thick Dense Foam chunk, since the Wood-one (for me, anyway..) ended-up splitting after awhile, since it was constantly being soaked / dried, etc...
So, use your 'press' to squeeze as MUCH water out as you can (ie:
Carefully 'step-Press' it down..) Then - leave it - on Top of your 'cake', as you
Invert the drain bucket, and tap-tap-tap the bottom / mouth of the bucket on the ground, until your Cake-log schloops out the bucket, and voila.. Ready to put up on yer nice hot roof / other-such drying area (..and obviously, protect from Rain, cuz that Will ruin yer nice Cakes!

ie:
And in a Day / Two, up-to a Few days (Ambient-Temps / Sun-dependent..) you'll have some nice 'Cake-logs' that you can stash away for, ya know.. Those times in dead of winter where - for some Unforseen reason - you just can't use your cut wood (Ie: got wet / not cured yet / ran out / got stolen / who knows..) and you're
also all out of Propane / Kerosene / etc, etc, and here you've got these Nice (effectively..) logs, that Do burn a
long time
(PS, If you're having Trouble burning, *cut them up* / slice / saw / chop, whatever.. More surface-area = quicker burn.. And, sure, you could add some accelerants / bit of sawdust / dip in wax, etc, etc.. I find it's helpful for the 'super-thick Cakes' ( >3" thick) to drill a large hole thru the center, to help with air-circ / drying...) They're Not really 'Fire
Starters' (cuz they're So dense..) but once 'going', they Do burn a nice, long time - like a Log..
These could also be good as barter-items, ie: if someone wanted your - Precious - Hardwood.. At least that's what I'd 'sacrifice', first.. Or, yanno - I just cannot imagine a Better 'gift' for that One nasty Ex than sending a 'frosted' one of these.. 'Happy Birthday, *****!'

Just kidding...
Last comment on any 'toxic contents'.. If you're *
Really that concerned*, you can make ones for Outdoor-burns with Newsprint, etc - and 'Indoor' / cooking / rocket-stove ones with Egg-cartons or Kraft / Brown-Paper,
Only.. (See those thinner, 'darker' ones in the top of those pics..) that's what we do with All ours, and they work great, and I've got to believe that what Little 'ink-residue', with what little is printed on cartons, is gonna be
So-minute after going thru this 'bath' - isn't going to pose a Huge 'chemical smoke' / Environmental-risk..
Maybe some 'chemist' will come in here and tell me I'm all washed-up

but.. That's what we've done with - quite a few - of them, and, well... I'm still here, typing, and no 'boils or emphysema or parts fallin off', so far...
Anyhoo, Fwiw.. Just seems a smarter thing to do with all that non-stop paper, vs just 'recycling' it..