Going out via New Fork Lakes gets you to a different trailhead. Do you have two cars? Another option would be to go south on the Highline Trail after your Titcomb Basin side trip and exit via the Pole Creek Trail, which gets you back to Elkhart Park. You could do a second side trip to Cook Lakes.
Entering from Elkhart Park, your first night will be at well above 10,000 ft. Unless you're already acclimatized to high altitude (as I recall you're from the midwest or east?), plan to take it really slow and easy the first few days. You won't have much choice!
We might cross paths; I'm going in from Green River Lakes on the 10th and exiting from Elkhart Park on the 19th. You'll probably recognize my dog from my avatar. Me--short, stout, elderly woman in a gray-green Sunday Afternoons Adventure hat which makes me look rather like a mobile mushroom.
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May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey