Whenever someone complains about height adjustment, the true problem is often due to the age of the deck. It isn't that the deck is too old but rather, it has been exposed to wear, tear, lack of maintenance, abuse, incorrect parts and a failure to set the deck up properly.
The thing is.....the LAST item on the list above often cannot be accomplished until all the other items have been corrected. There are decals on the deck that say "NO STEP" but people step on the deck anyway and don't realize that they are often bending the very pieces that control the cutting height. The gauge wheels are there to hold up the rear of the deck at whatever height the Operator specifies on the adjustment lever but if there has been bending/twisting to the adjustment components, then the numbers on the height adjustment are no longer correct.
Other issues can be badly worn/elongated holes in the mounting frame for the deck where badly worn pins go through. Worn out or WRONG gauge wheels will also upset the cutting height. A mower deck is no different than the engine in a car. If you want it to perform like new, then you have to repair it back to "like new" condition. If you were to price a brand new RM 44 deck for you Ingersoll, the price at the dealer would likely be around $1400.00 plus. You own a premium tractor with premium components. Most of the rebuilding process is labour. You have to drill out the oversize, irregular shaped holes and put bushings in them along with new pins, washers and hairpin clips to hold them in place. The rotary mower parts manual in the Tech Section will show you what parts were used originally to manufacture your deck.
The Operator's Manual, also in the Tech section, will guide you on how to set up your deck so that it cuts the way it should.
You do not mow in the Float position. You lower the deck to the ground and then centre the bell-crank lift pin in the long slot of the lift link. That allows the deck to float up and down instantly with no interference from the lift cylinder. This is why those long slots are there. The deck cannot move oil in or out of the lift cylinder fast enough when the tractor is at mowing speed.
We can't tell you what's wrong with your deck because we are not there to view it, to make measurements, to use straight-edges, levels, measuring tapes, squares etc to check all the known problem areas. That's up to you to do. Common sense tells you when a hole is round and snug-fitting compared to one that is more of a slot than a hole. The instruments mentioned will help you determine what is bent or not square or does not measure the same on both sides. Maybe you have the wrong diameter gauge wheels. Maybe the wheels you have are so badly worn out, they don't support the deck properly any longer.
Feel free to ask more questions.