Many 444 Marlin shooters on this board. I believe the 240-grain bullet is the best compromise for deer. I have not shot deer which weighed over 180 pounds on the hoof with the 444 marlin cartridge so I cannot speak of its performance on big deer.
The 270-grain Speer Gold Dot bullet is an excellent compromise between weight and bullets which will open up readily on light-bodied deer while retaining a good amount of weight for penetration.
I have killed a good number of cull deer with the 240-grain Remington bulk bullets and they perform very well on 125- to 130 pound deer.
Your velocity goals for the 240-grain bullet in the short barrel are easily met with a variety of powders. From my 17.5” barrel Winchester these are good loads.
54.5 grains of IMR 4064 1,845 fps
53.0 grains of IMR or Hodgdon 4895 1,875 to 1,895 fps depending on the brand of powder with Hodgdon a bit faster than IMR.
53.0 grains of IMR 3031 1,901 fps
56.0 grains of IMR 4320 1,929 fps
39.5 grains of IMR 4227 1,978 fps
If you want to push the 240-grain bullets a little faster:
47.0 grains of Hodgdon 4198 2,108 fps
52.0 grains of Hodgdon 322 2,109 fps.
54.0 grains of Hodgdon Benchmark 2,119 fps.
My go-to load for the 240-grain bullets is 49.2 grains of Hodgdon 4198 which gives me 2,257 fps and excellent accuracy. This is a loud load and it gives me a good tongue of flame up through the ports on gray days.
For good plinking and practice loads using Alliant Unique and 240-grain cast bullets:
16.2 grains of Alliant Unique 1,495 fps
Using IMR 4227
30.0 grains of IMR 4227 1,615 fps