The Dashwoods arrived in early September. Colonel Brandon met them shortly after they arrived--about three days. We know that Sir John came to see them every day for the first two weeks they were there, and Marianne meets Willoughby in the third week after they arrive.

Since Marianne showed not the slightest glimmer of interest in Brandon during those two weeks, and since he was not even there every day of that time, I can't imagine when or how he had "a good deal of time" to court her.

I don't think he thought his 2000 a year (not 3000 a year) was incentive enough to get a young and very beautiful young lady to change her mind about him within a matter of days.

Also, despite Mrs. Jennings' conjectures to the contrary, he did not necessarily fall in love with Marianne when he first laid eyes on her, either. Elinor saw no sign of it at all until after Willoughby was on the scene. I think he was quite of Marianne's own opinion about second attachments to begin with, and never imagined himself attached to anyone else again in his life. Considering their age difference and Marianne's indifference to him, he probably fought his inclination too. I don't think he even entertained a thought of 'courting' her.

Also, unless Eliza's child had no name for the first three years of her life, her mother named her, not Colonel Brandon. He never saw the child or took her as his ward until she was 3 years old.

When Colonel Brandon found out it was Willoughby who had seduced his ward, he was also firmly under the conviction that Willoughby was engaged or nearly engaged to Marianne. Every one of his acquaintance told him it was true, and he even heard it from people who were not connected with the ladies at Barton Cottage. Willoughby had already made his refusal to marry Eliza absolute. Telling the Dashwoods on him was not going to alter that. However, if he told them and it caused a breakup between Willoughby and Marianne, she would be miserable and hate Colonel Brandon forever, most likely. By all appearances up to that point, Willoughby's feelings for Marianne were sincere and he did not intend to abandon her. Had he really loved her and married her, it was not necessarily a certainty that his treatment of Eliza alone meant he would be a bad husband to Marianne. Brandon hoped she might 'reclaim' him. If he married her, she might also convince him to do right by his illegitimate child with support or whatever means. I don't think the decision was as clearcut and obvious as you make it out to be.

As for going to India--he hoped their marriage would not go to pieces. He left in the hope that the two of them could learn to be happy together if he were not on the scene. If he had stayed in London, would Eliza still be expecting and hoping to see him instead of learning to love her husband? If Brandon was 'keeping tabs' on their marriage, would he be giving their marriage a chance?