What type of new tires? R4's? They are stuck monkeys in the woods. (I know!) Get yourself a GOOD set of chains that won't fall between the treads. MOST chains will fall between the treads of R4's and make them WORSE in the soft areas as they will fill with goo. Get some with rings, etc that will stay on top of the tires. Then you will have to still be careful of the boggy spots. If you have a 3pt rototiller, they are good
ballast and can get you unstuck. As long as the way forward is clear. The extra forward push from the tines as it runs has gotten me out of more than a few areas.
Do you have a hand crank come along? Get one. A GOOD one. Then get 1 or 2 (2 is better) nylon tow straps and a 25' chain. I've got many a fond memory of cranking the tension up on the come along, then jumping on the tractor backing 18", jumping off and cranking over and over and over again. I welded up a winch box on wheels. Basically 2 levels, bottom holds the battery, top holds the winch with attachment points for chain. The winch has remote key fob control. Easier than the hand crank, but bulker to carry.
On the weights, if you don't have them, the front will sink farther and the traction will be even less. You may be getting stuck because you don't have enough weight still. Every pound on the loader takes off 1-2 pounds of weight from the rear end. Depends on the tractor geometry. That will allow the tires to spin easy and dig a hole. You should have weight equal to 1.5x the lift capacity of the loader
or more. A large heavy weight on the 3pt, tires filled and wheel weights are normally all needed. The 3400 loader is probably rated at 2000 to 2200 pounds, so you should target 3000-3500 pounds of total weight. Yeah, it's a lot. 2wd loader tractors need all that and more!