Ryan'smilling
Addicted to ArboristSite
Here's one that's cheap enough to experiment on!.....
https://www.ebay.com.au/itm/Stihl-034-Cylinder-MAHLE-46ZN3-stihl-1125-OEM-BoxHT52/173214729888?hash=item28546706a0:g:yVYAAOSwNOJap90A&LH_P
Is that a super cylinder or just a standard 034? They're not the same bore.
Overkill, yes the 034S is said to have better port timing. I believe it, but there will still be some variation between individual cylinders (both 034S and 360), so there's no guarantee that you'll be making an improvement by swapping them. It's likely, but not certain.
Honestly, I think it'd be a waste of time and money to swap them. If you can't wait for the 462 and haven't caught the Husky bug yet but still need to spend some money, send that saw off to be ported. Or your 241. Yes, it'll cost more than swapping a cylinder, but you'll know for sure that you're gonna end up with a very fun saw to use with a lot more pizzazz than a stock saw.