I'm not a trained gunsmith, but I shoot CAS and have learned to do a lot of my own "tuning" on my cowboy guns - everything except touching the sear itself.
Likewise, while I have a collection of 92's, 94's, 60's, 66's and 73's, I very much prefer the Marlin 1894 for CAS and have had the least amount of issues with it. It is easy to disassemble, clean, tune, and the timing of the internals is rarely an issue.
Without seeing the gun, and knowing how old it is, what has been done to it already, etc... I can only make suggestions.
1.Is it a new gun? If you must be firm or harsh with the lever, that gun is not smooth or slicked. An older, well-worn gun is already partially slicked up. I just bought another 1894C and could not believe how stiff and sticky it was from the box. I took it apart, cleaned it, and then lubed the internals with valve grinding compound. Then I sat in front of the tv for the evening working the action and dry firing it. By the end of the night I had "shot" the equivalent of several thousand rounds and it was already smoother. I then took it apart again, cleaned it well, and took it to the range. Now that it has a legitimate 500 shots through it, I was ready to do some basic tuning. I lightened all of the springs in it, and polished the moving parts with a stone where they were showing signs of wear. I did not touch the trigger and sear. It now has a smooth action with a hammer that still fires every shot, but with a 2.5' trigger. I will soon be changing over to a one-piece firing pin, and someday will have the sear polished to get rid of any creep. Oh, I also shortened the trigger by an 1/8th of an inch, rounded the sharp edges and polished it, so that my finger doesn't get bitten while working the lever fast. I can now get 10 reliable shots on the paper at 20 yards in under 4 seconds without even working hard.
2.Type of Ammo. You've already said that you have tried every type of ammo, but always stay away from wad cutters or semi-wadcutters with lever guns. On toggle rifles the round is lifted up while it is horizontal, but with all others the cartridge is lifted at an angle and must be able to feed smoothly into the chamber. Marlins are must more forgiving than a Win 92 or 94, but they too prefer round nose or round nose flat point over anything else. Work the action slowly and you can get away with other ammo, but in CAS on the clock, forget it if you want reliability.
3.Length of Cartridge. Are you using reloads that are a little too long? Again Marlins are more forgiving than 92's or toggle rifles, but it can still be an issue. Check the length.
4.Magazine Tube/Spring. Is the bullet getting hung-up on a little burr, or is the spring too weak to get it started properly, but you are only noticing the problem once it gets to the top? Does it start dragging at the bottom? Remember, that bullet must come out of the tube fully before the lifter tries to raise it. If in doubt where it starts to catch, paint the bullet with some coloured nail polish, work the action, and then check for colour inside of the receiver.
5.Timing. The timing on a Marlin is nearly foolproof, unlike some other lever guns. However, if it is a new rifle it is possible that something from the factory is not right. They test fire them to ensure that they go off, not to make sure they actually work the way they were supposed to. If it is an older gun, it's possible that something inside is worn or bent.
I hope this helps. Do not believe that you must be firm with the lever. If it requires any positive action or force, it's not ready for CAS.
JB