When you are speaking of SCH DPS limits, there are things you need to take into account, such as:

A) Is there lots of Baneing to be done to inflate DPS?
B) Can the SCH autoattack? (Ie. be stacked on the boss without any complications)

A inflates DPS a ton, whilst B adds up a few DPS depending on the encounter and the duration for which you are stacked on the boss and can afford to spam Ruin 2/autoattack.

Then we would also have different encounter types:

1) A completely trivial encounter where literally no heals are needed (barring Embrace, Regen and maintenance Curing) and the SCH can DPS 100% of the time without burdening anyone by doing so.
2) An encounter that has its healing spikes but wherein the WHM can effectively soloheal some phases/most of the fight with only a mild strain on their resources (ie. no Ballad needed still), by not having the SCH be on top of their healing game. That is, if the WHM is good.
3) An encounter that has its healing demand spikes, but wherein the SCH in question can still DPS a lot while on top of their healing game that is required of them, without making the WHM MP-strained.
4) A heavy encounter wherein both healers are needed for nearly constant heals and wherein the SCH can only drop a few dots every now and then or then severely ignore their healing game, as a result making the WHM MP-starved.

#1 is just that, a trivial encounter. #2 will speak you more about your group's WHM's skill as the SCH-rotation is not exactly rocket science. #3 is the zenith of Scholaring skill-wise, even if the numbers will be less inflated than in the other cases. #4 usually translates to progression or heavyass fights where the SCH only dots when possible to meet the DPS checks (ie. undergeared T13).

So with that being said, it's not always in the numbers, but also how the encounter plays out and you'll need to understand that your numbers change depending on the approach you take.

300 is achievable at i110 w/ a 115 weapon without songs and Bane inflation, if you're autoattacking as well. To go higher than that, you will need to account Foe Requiem (with stacked bards, even better!). If you want some reference point for a semi-challenging encounter that is not a dummy; I was hitting 230 DPS at i110 with a single bard on T9, with the #3 approach I described in this post.