I just read this for the first time.
Since the surge lessens when you choke, there might be an air leak. But it's not so likely unless the shop that you paid for the jet change just did nothing and handed back your machine. In that case what you are calling a backfire is a lean pop.
Confirming or denying the air leak could be a pretty quick check though. Check that the bolts that hold the carburetor to the engine are tight, Not Hulk tight just good and tight.
If they are ok (likely) you may have a piece of debris in your carburetor or something sticking to cause wrong movements between connected links.
I am comfortable with carburetors but they can be daunting.
Since you are feeling handy, I'd recommend go through that carb check sheet.
Here is a gasket kit
Honda 16010ZE2A20 Gasket Set - Jacks Small Engines, Use original equipment.
To disassemble your carb for a full internal cleaning.
Take pictures of the linkages and wires. Turn off the fuel supply, and drain the fuel using the angled screw under the bowl. Don't disturb the governor, just use a little hook or pick to carefully and gently remove the links from the governor.
On some carburetors I have had to unbolt the carb to turn it in such a way as to remove angle links without bending them. Remove the carb and take it to a clean spot to take it apart.
Those ultrasonic cleaners are terrific. Just don't use solvents on rubber parts.
If there are any welch plugs they are kind of a pain to deal with, I'd leave them be at first. If the result does not change
then I'd remove them for further cleaning.
Someone somewhere can give you the starting points for where to set your jetting screws after reassembly. Think someone even posted it in an earlier thread.
Steve's Small Engine Saloon has a really good video on how to find the Sweet spot on carb setup.
If you aren't comfortable with fixing it yourself, or if you don't want to spend the time, the carb I looked up was $108 plus shipping. But there are 6 different HSS1332 versions in the lookup so you'd have to verify. I looked in jackssmallengines.com.
I grabbed the carb part number from the first blower on the list and googled it. None at ebay right now, but it is February, high season.
Or, find a small engine place near you to do the repair. That blower is too fine a piece of gear to leave unrepaired.