Temp alone cant be used as an indicator of success regardless of what many will have you believe. You have to look at everything.
The fact the individual is clearly feeling the effects of lack of synthroid tells me something still isnt quite right.
desiccated supplements are often not a 100% replacement for synth and just as when a person goes on synth it often takes a lot of trial and error to get things dialed in which is a constant moving target.
Remember that just because Iodine and other nutrients are added it doesnt mean the body is efficiently using them.
As previously mentioned, someone on synth has relied exclusively on synthetic T3/T4 which means their thyroid has basically stopped functioning.
You cant expect to get a broken arm out of a cast after 6 weeks and have it function at 100%, it takes time to restore coordination and muscle tone. Often times longer than it took to atrophy in the first place.
This is why I often caution people when they talk about going on synth hormones to begin with. There is no shortcut to recovery, it takes time for the body to heal and start working as intended when nutrient levels are restored. This will not occur when external hormones are being added.
In an effort to maintain homeostasis the body has various feedback mechanisms to monitor hormone levels when the levels appear high due to consumption of external hormones the body reduces natural production.
I think the desiccated products are a better choice BUT you are still in essence introducing external thyroxins and preventing proper thyroid function.
If it were me, I would make sure a full and complete supplement plan was in place. I would have Iodine sufficiency tested with a loading test and once found Iodine sufficient I would slowly over the course of weeks taper off the synthroid. Knowing that there is going to be some discomfort. How long this lasts depends but generally speaking the longer the thyroid function was suppressed by external hormone sources the longer it will take to recover.
During this transition I would probably get thyroid labs done monthly to see whats going on in response to the lowering dose of synth. If they make it through all the way to cessation of synth and the thyroid still doesnt seem to be responding based on labs, temp and how they feel then I would introduce the desiccated product slowly building the dose while monitoring temp, labs and how they feel to try and get them to a comfortable spot.
This scenario does highlight why I often suggest people try and deal with a sluggish thyroid BEFORE going on snth because once they do it can mask real thyroid/nutritional issues and can be much harder to reverse or address in the future.