Ductless vs. Modulating Furnace to deal with ductwork noise

My house has a lot of ductwork noise throughout the house whenever the heater is on. It isn't a problem in the summer with the AC. In the winter, I get tapping and popping noises from multiple places in my house and it is driving me nuts. It starts after the heater is turned on and continues for awhile after it has turned off. I have had people come out to my house and check on the pressure of my furnace and to see if they can secure any of the exposed ductwork, but it hasn't worked.

I have been told that I can put in a ductless mini-split system in my house for $19,500 or I could try switching out my furnace (which is quite old) with a modulating furnace (SLP99 Modulating Furnace) for $9,800. I am quite torn by this decision, because just replacing the furnace is cheaper, seems easier and would heat the home more evenly, but I am afraid it may not resolve my problem. Has anyone encountered this issue before and has a modulating furnace fixed the problem? The HVAC professional I worked with said that it would fix the problem by heating and cooling down the ductwork gradually and by always blowing room temperature air through the ducts and thus prevent the ductwork from getting too cold.

source https://hvac-talk.com/vbb/threads/2242842-Ductless-vs-Modulating-Furnace-to-deal-with-ductwork-noise?goto=newpost