This is a tough question to answer, and I think a lot of it has to do with awareness of your capabilities. I can't tell you what you are capable of, but I'm applying in the current cycle and had a roughly similar situation. Maybe it will help?
I took the MCAT on July 13 this year, submitted TMDSAS on July 19, and was verified on August 12 after I went through the residency review deal. I chose to study for and take the MCAT in July because... it's the MCAT... and it scared me... I had my TMDSAS essays done from the spring semester, but other than that I didn't even start working on my application until July 16. I'm not sure if that's late by real world standards, but it's late in comparison to the time lines you mentioned. Also, I didn't know about the secondaries because I don't know why, so I didn't get those in until late September.
It's hard to say what effect this has had. For what it's worth, I got an II at UNTHSC ~2 weeks after I was verified on August 12. I got an II at San Antonio ~6 weeks after I was verified. Given that I finished the secondaries for the others 2-3 weeks ago, it's not surprising I haven't heard back yet. Houston and Galveston haven't responded, though they didn't have secondaries and so have had my application since August 12th.
I don't know what your application looks like, but here's what I would suggest you take into account:
1. They will still look at your application, even if you submit it later. Don't waste time, but don't kill yourself trying to meet the "DayOneGo" SDN standard. You can get love from TX schools even if you push it back!
2. The MCAT sucks. I had the same plan in mind as you originally, and I was only taking Orgo 1 and an EMT course. I think nailing this test is important though, and you need prep time. I studied from the time my classes ended in May to my test date in July and ended up with a 36. The feedback I've gotten thus far suggests medical schools would rather see you knock the MCAT out of the park than submit your application ASAP. 1-2 months of solid, uninterrupted summer study can make a really, really significant difference in your score.
3. I found that the application process takes much more time and effort than I thought it would, though you might not need as much time. Maybe you can handle it and not let it affect your classes or ECs, but why do that to yourself?
4. I think that for the most part the application is either good enough that they will look even if you submit later, or weak enough that you probably need the time to shore it up anyways. Either way, I don't know that submitting immediately does anything for you.
I won't lie to you, I was stressing pretty hard about submitting so late. Take my experience for what it's worth to you, because only you know your qualifications, the caliber of your PS, and so on. Based on my experience, and given that I haven't been accepted yet, this would be my suggestion:
A home run in the first inning is nice, but a grand slam in the fourth inning is better. Focus on the fundamentals of your application (MCAT and spring classes, as well as any ECs you're still doing), and get to your app once you've taken care of business. If that means delay, so be it. Schools will be around when you finish, and there's always room on the team for the guy/gal hitting the grand slam.
Either way, good luck!
