Ha! I thought you said you didn't fall off the turnip truck, or was it that you didn't fall off yesterday, but you must have fallen off at some point in time to give you a vastly different perspective of the 444 Marlin than most of us who have been shooting it for the past 40-50 some odd years. And yes, I agree, you are older than dirt. You said so yourself.
Actually, I tried that idea a long time ago but I can't give you any real accuracy data or results because I either didn't keep them or the darn things didn't shoot for snot. I a 24" Marlin, one of the first ones to come out in 444. The bullets were soft and copper fouled the barrel because they were 44 magnum bullets and were being shot down the barrel better than 1,000 to 1,200 ft per second faster than they were designed. The same happens if you load any bullet designed for the 44 magnum down a 444 Marlin tube at Marlin velocities. Then it's a real royal pain to clean the copper fouling out of the barrel, especially if your barrel has micro-groove rifling with a 1:38 twist. I recall the loads blasting out with significant muzzle flash but don't recall if they were accurate at all.
None the less, I used to take whatever 180 gn slug I had around for the 44 magnum and load it into the 444 using 4198 powder. 49 gns of 4198 used to get 2,400'/sec with a 225 gn bullet, and I used to add 2 gns powder weight for the reduced weight of the 180 gn slug from the 225 gn slug. I do not know how fast they went but the latest issue of Handloader Magazine ran a very full article on the 444 and provided a ton of data that may interest you. In particular is a load for 180 gn Sierra Jacketed Hollow Cavity bullets over 51.5 gns of IMR 4198 for 2,585'/sec from a 22" barrel.
None the less I caution using 44 magnum bullets in the 444 Marlin at 444 Marlin velocities. I really doubt they will come apart in the barrel or in flight for that matter but they will leave you with some nasty copper fouling in your barrel and what happens on impact may not please you if you don't have a clean pass through shot. At Marlin velocities the bullet may be pretty frangible and not give you the penetration you want for a clean end to a sick animal. You can probably load them down to 44 magnum velocities for light shooting loads and still have more than enough ooomph to do the job cleanly. You did not mention the distance at which you were thinking of shooting but I would feel quite comfy with loads like that on Coyotes to 100 yds or better, if your rifle shoots them accurately.
Also, depending on your barrel - many are still made with the micro-groove rifling (12 lands and grooves instead of the Ballard Cut of 6 lands and grooves and a 1:38 inch twist instead of a 1:20) you may wish to consider fire lapping your barrel. If your barrel is longer than 22" you will get a additional boost of speed but probably more fouling too. The fouling isn't a accuracy killer right away but it needs to be cleaned out.
Veral Smith, one of Graybeard's forum moderators and contributors down in the cast bullet section is a expert at fire lapping or bore lapping barrels and has written a book about it and I believe provides the means and instructions to fire lap your bore for greater accuracy and the use of cast bullets. Another expert in the field of fire lapping is Marshall Stanton of Beartooth Bullets. He too has penned a manual on the fire lapping process and provides materials and instructions on the 'how to do it'. He has also conducted extensive research with the 444 and cast bullets. It is really worth the read to get to the Beartooth site and read his data and results on the 444 with cast bullets, read his notes and his load data, it is well worth it.
As a side note, I have used the standard 240 gn Remington slug in my 444s and get excellent accuracy from my fire lapped Winchester Big Bore in 444 with the micro groove barrel but even though fire lapped, the darn thing still gets copper fouling when I use bullets made for pistols. Those bullets perform effectively enough on Whitetail but seem a bit 'tender' for use on anything larger. The 265 gn and 300 gn slugs made for the 444 are whompers on larger game. I have used the Beartooth 335 gn and 350 gn cast slugs on Elk and Hog and it was a 1 shot affair, and that was with my 26" custom Winchester 94 in 444. Most often I use 300 gn Beartooth cast slugs right at 2,300' from my 20" rifle.
If you can get a copy of the December-January 2019 Handloader Magazine and also get into the Beartooth Bullets website for some incredible data on the 444, you should go for it. Now you can mess with this nonsense.....Just sayin'