Although it's rarely if ever heard in speech, the form of that clause where "that" comes at the start of a sentence is perfectly correct. We do not need to pause to make this sentence make sense. Adding commas seems to suggest that "Mycroft is planning to send Enola off to a grim finishing school for young ladies" is a subordinate clause, but it isn't. Without it, we don't know what "That" is talking about, so it can't be omitted.
When "that" comes at the start of a sentence, we can't omit it from a that clause. Without "That", the sentence doesn't scan; we can't understand the connection between Mycroft's planning and the incentive. The purpose of "That" is to connect the two ideas, to say explicitly that Mycroft's planning provides an incentive.
This type of sentence is pronounced without any pause after "That". The "That" should be taken to be part of the phase it opens. The comma you placed after "That" is, I would say, definitely wrong, and makes the sentence difficult to understand. The second comma you suggested, after "ladies", is probably just unnecessary.
Here are some more versions of that sentence, with the same meaning:
As two sentences combined with a semicolon:
Mycroft is planning to send Enola off to a grim finishing school for young ladies; that offers an added incentive to get away.
With the that clause in a more conventional position (note that this needs a "preparatory it"):
It offers an added incentive to get away that Mycroft is planning to send Enola off to a grim finishing school for young ladies.
Getting rid of that entirely (note that this needs some verb form adjustment):
Mycroft planning to send Enola off to a grim finishing school for young ladies offers an added incentive to get away.