Always good to see some choke in Towers! I agree, this is a good looking deck. I think you're right to want to replace
Final Count and
My Axe Is Notched -- with only one copy of each you're likely to get no use out of it at all. Two copies of
Sting, Baggins Heirloom instead will make a big difference for Frodo. I'd also try to find room for at least one copy of
Severed His Bonds as an emergency for the last 3 sites. Getting 10+ strength on the Ring-bearer isn't a great challenge for sites 7-9 with 3 companions and it'd be a shame for that to be all it takes. 14+ is substantially harder, and 21+ is nigh on unachievable.
Come Here Lad has a problem: you have no way to retrieve the stacked cards. Odds are you'll losing a key card for FP or Shadow nearly every time with a deck this small, too. May as well use
Search Far and Wide if you need to dig for cards, or even better use those slots for
Severed His Bonds. The only other note to make is that Legolas is probably gonna be exerting Gimli or taking hits more often than not.
Courtesy of My Hall could bring back a copy of
Toss Me and/or heal Gimli in a pinch.
Stout and Strong might be useful to help Legolas out as well? Then again if Legolas loses or exerts Gimli every site and Gimli wins his skirmish every site the sanctuary healing will be enough... I guess you've thought this out already
Shadow side is nice and straightforward. All I would do is remove 2 copies of
Nasty, Foul Hobbitses (useless at the start of the game) for
Men of Rhun. Oftentimes players (especially with Rohan decks) will risk assigning Frodo to avoid burdens from
Vision from Afar or Easterlings. I have lost this way at site 4 plenty of times myself, haha. I'll be interested to hear if
Southron Commander is enough for Ringbound Ranger decks.