That looks and sounds right.
Goes without saying that to remove it be very careful...slow and deliberate as you approach each step...don't force anything, etc.
And appended below is a consolidated list of proven tips from many users as a barrel removal guide.
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Pinned Barrel Removal Guide, tips from multiple members consolidated into a list for convenience.
( from tips offered by many members on the ALR and MLF muzzleloading Forums )
1. Firmly secure muzzleloader so it can’t move
2. Remove the lock and tang screw
3. Tips of barrel pins should be rounded so they don’t catch / splinter wood
4. Use 1/16" (for small pins) or 3/32" (for large pins) straight punch, no taper, “cupped face” if possible, same size or smaller than pin diameter
5. If barrel pins are ”˜tapered’ they must be installed / driven in from the correct / same side each time.
6. Pins are driven in until they’re flush on their entry side then gently recessed.
7. Their length should be so they’re barely also recessed on the opposite side
8. Pins are removed by pushing them back out towards the side they entered from
(if straight pins are used, it’s less important, although possibly a good regimen to follow regardless)
9. Coat the bottom of the barrel and the channel with a good wax/rust preventative grease like RIG
10. Coat pins with beeswax to protect holes and help keep pins from sliding out
11. (Optional) Use a hand squeeze clamp with rubber ends and a scrap piece of “soft” wood about 4” long. Clamp the wood over the pin hole on the exit side of the stock.
Drive pin slightly into the softer wood just enough to grab it with fingers or pliers. Remove backer wood and pull out pin. Before reusing pins check and re-polish as needed
12. When pins are removed, maintain their position and direction as they are usually different lengths
13. Go slow the first couple of times you remove the pins. Barely start them out, and look to ensure you’re not raising a chip-out. If you are, apply glue and press the chip back in place. After it is dry, hold the area in place with a piece of wood and carefully try to ease the pin out. Once the pin is out relieve the interference slightly.
14. Now that the pins are out (tang screw should already be out) while holding the barrel firmly in place in the stock, turn the gun upside down (stock up barrel down) on a padded workbench or table. Gently bump the butt of the stock UP. The object is to get the tang to drop free of it's inlet before the muzzle end moves.
If the muzzle end is lifted first, the wood at the end of the tang inlet may be chipped out / damaged, particularly if it is a tight inlet or barrel has moved back a bit after firing heavy loads.
The above are the tips supplied by other good people willing to help...I just put them into a quick reference list for this very purpose.
Along the way I’ve added some additional tips of my own:
1) Leave a strong ramrod in place to add some extra spine / strength to the thin fragile forestock;
2) I put a very slight bevel on the under side edges of the tang tail so there's no sharp edges to catch the edges of the of the tang mortise.
3) I lay the stock belly down on my carpeted workbench and drape a 25lb bag of skeet shot over the butt stock to hold it solidly immobile;
You could do the same with a hefty sand bag, something like that...because having both hands free to guide the barrel is obviously very important;
4) I slide a piece of wooden dowel into the muzzle, leaving several inches sticking out from the muzzle as a handle...thumb pressure down on top of the barrel flat in front of the front sight.
The other hand is holding the barrel further back guiding the tang tail carefully into place.
