Most of the early 044s had C3M carbs. I don't know why the HD-11 is not listed, they had .070 jets and were used on the heated handle saws.
HD 11s are NLA, but I recently picked up a couple of HD-14Cs on ebay. They do not have limiters, and I believe they are also .070 jet.
Although they physically interchange, many of the 044/440 carbs (and AM carbs) have a smaller venture than the true 046/460 carbs.
I opened up the venture with a grinder on an Asian carb that was on a Asian 440 big bore and it helped a little. I also learned that you don't grind that feed tube that goes into the venture. Part of the reason I like playing with the Asian stuff is that your mistakes are not nearly as costly!
$20 is a lot less than $80!