I agree with you but there are only so many spots available. Leivo, Percy and Harrington would have to the minds of the coaching staff. I see Brown, C. Carrick and Corrado making the team before these 3.
Since Connor Brown can go up and down freely without waivers, here's what I'd do.
Let's say he has a grest camp. Send him down and tell him that Leivo needs a chance first. Tell him he's the first injury call up. Tell him he's for sure getting called up by Christmas or the trade deadline (unless his game falls off a cliff).
When the time comes, hopefully Leivo looks good and you can trade an upcoming UFA (Michalek Greening Laich) instead to keep both young guys. Or by that time Leivo looks good and he himself has trade value and gets shipped out to make room. Or Leivo looks bad and you waive him to give Brown a spot but at least he got his chance.
Strictly speaking in the short term here (October to December), I hope they send down every guy that doesn't need waivers except for Nylander. Bring up kids when injuries happen. The folllowing roster is 24 guys (one injury or one guy ends up on waivers).
Bozak Kadri JVR Komarov Lupul
Michalek Holland Greening Laich Froese
#11 - Nylander (doesn't need waivers)
#12 - Leivo
#13 - S. Carrick
#14 - C. Smith
Rielly Gardiner Hunwick Marincin
#5 - Percy
#6 - C. Carrick
#7 - Corrado
#8 - Harrington
Bernier (goalie#2)
Injury call ups (in order)
-Connor Brown
-Brendan Leipsic
-Viktor Loov (D)
-Garret Sparks (GK)
-Soshnikov
-Leipsic
-Hyman
-Kapanen
-Bibeau (GK)
-Valiev (D)
-Gauthier
If we want to also sign a UFA frward (Stamkos/Backes/etc) we can always move Holland or Percy for a pick. If we're lucky we could move an older guy like Michalek or Laich instead and keep our younger guys.