Will you be eligible for the new employer's insurance effective October 1? If so:
You have 60 days to elect COBRA, and if you do so it automatically goes back to the day you lost regular coverage.
As long as you don't have a break in coverage that exceeds 63 days (federal law), there are no preexisitng conditions.
So what you would want to do is hang on to your COBRA election materials, and if you have a medical charge that exceeds the cost of the COBRA premium between now and October 1, go ahead and elect COBRA and the procedure will be covered, even though you waited to enroll after the medical charge was incurred.
If no signficant medical charges between now and October 1, you simplly go w/o coverage for what sounds like 6 weeks or so (key is less than 63 days) and pick up coverage on October 1 with no preexisintg condtions.
Having said that, most company health plans have a waiting period of at least 30 days, so in that case your best best is to get a short term policy in the interim. But even in that scenario, you'd be fine to start coverage as late as October 1, b/c again you would not have exceeded the 63 day break in coverage.
You'd be smart to get someone who you know that is well-versed on insurance and the new health care laws to confrm what I'm saying (possibly the benefits person at your new employer), but I'm confident that this is correct.