So with another RHC faceoff specialist (let's use your example - Beagle), then our lineup is something like:
Maroon - McDavid - Draisaitl
Lucic - Nugent-Hopkins - Eberle
Caggiula - Letestu - Kassian
Pouliot - Beagle - Slepyshev
So when there's a big draw that requires a RHS to take the faceoff, you've got your choice of Letestu and Beagle. But if that faceoff requires a LHS, it's still McDavid or Nuge, our 2 worst FO men.
I'm not against adding another RH FO man for the bottom 6, especially if he can play wing (then you have 2 on the ice at once). But what I'm saying is, in a perfect world, if you're adding a player who can win draws, it would be better if he was a LHS.
Letestu is not a good even strength player. For an 82 game season that third line would struggle mightily. Guys like Beagle, Boyle, Vermette, etc, etc should be targeted at the trade deadline when the games start to get tighter.
That third line is most likely going to be facing third line competition for the majority of the regular season. So adding a guy who can provide a boost of offense without getting caved in defensively should probably be sufficient.
That third line this season was centered by Drake Caggiula and he had a laundry list of linemates. That shouldn't be too difficult to improve for the short term.
My vote goes to Ryan Strome. He gives a bonus of being a second one-time option on the PP and is likely very attainable.