1) Paeon returns 30 tp every 5 seconds. With some math, it takes 30 seconds for your melee to gain access to 2 abilities that they would have had to wait longer to gain access to. It is roughly a 2-5 dps increase to the melee if it is sang multiple times in a fight. Foe will increase the raid's damage buy a lot more then that. Unless someone has died, Foe has priority. Your melee needs to learn how to control their TP.
LOLWUT
WE CAN SKIP A DREAD, BUT LET'S CONTROL OUR TP !!!

Do you want some "real" math ?
-Every 18s you are using your 2 dots : 2*80 tp. It will be every 17.5s. 2 out of 7 GCD's are these dots.
-Every 20s you are using Straight Shot : 70 TP. 1 out of 8 GCD is this buff.
-When the dots are up and the buff "Straight Shot" is up, you're using Heavy Shot : 60TP.
Let's imagine that you are unlucky with the RNG and never get the critical "Straight Shot".

With ZERO SKS :
56 GCD : 16 skills at 80TP, 7 skills at 70TP and 33 skills at 60TP. Total : 3750TP -> 67TP per GCD.
Every GCD, we're getting 50 TP and let's add invigorate : 400TP every 120s -> 8.33TP every GCD. Total : 58.33 TP recovered every GCD.
Net loss : 8.66TP every GCD. We are out of TP after 116 GCD, i.e 289s.

Well, a BRD could "manage his TP" by not using his dots Yeah, I'm sure Bloodletter isn't a big part of our DPS
And by the way, Paeon is 42.8% more TP restored per GCD. I don't know how you are doing some "math", but in a perfect situation, 42.8% more TP = 42.8% more DPS.