Ihe TSX 361 was designed for a 12O cu in displacement engine and your TO-35 has a 134 cu in Z134 IIRC. You need something to handle about 12% more airflow.
The best thing to do is to find the correct carb for you tractor.
You could probably use a TSX 458 from the Z129 powered TO-30 and adjust it adequately because there is only around 4% difference in air flow and the TXS 458 has the larger venturi.
Having said all of this, if the tractor ran fine in the past with a TSX 361 I would suspect the poor running condition you are experiencing now is due to either a dirty carb or a poorly maintained ignition system. How have you concluded that the carb is the problem in the first place? Most poor running issues that are blamed on carbs turn out to be ignition related! So check you spark and see if you have the requisite FAT, BLUISH-WHITE SPARK, the color of lightning. Check the distributor shaft for wear and check the initial timing.
You said your carb had a lot of rust in it. It"s likely unless you soak it in carb cleaner of over 24 hours and then blow out all the passages to make sure they are flowing freely, you still have some crud in your carb"s metering passages. You may have to manually clean some of these passages with small wire to get 50+ years of crap and corruption out of these passages. Make sure that you set the float correctly because the float setting on these carbs in important. Always shut the tank valve off when you shutdown to preclude fuel leaking from the carb.