Disclaimer: The below is not a recommendation to violate the terms of an employment agreement or violate any laws of any sort.
To minimize risk of violating your moonlighting clause, I would recommend:
- Consulting an attorney
- Doing work unrelated to your day job
- Building a business that can support you without a day job
Your contract may not only contain a clause restricting your right to do outside employment, it may contain a clause that says the company owns the right to your work even if that work is done outside working hours. Depending on your jurisdiction, the company may be able to claim consequential damages or at least take you to court and make your life miserable even if they know they will eventually lose.
These could all cause more harm than the current high-interest loans you want to start a side business to pay back.
Consult an employment attorney before doing anything with the side business. Give the lawyer your employment contract and any other relevant material. Make sure you fully understand the legal consequences under the law and under your contract for the violation. This will cost money, but it is money that will be well spent if it prevents you from making a colossal blunder that costs more than you'd make off the side gig.
If you do get caught, there will likely be a range of consequences. As you said yourself:
The climate in my particular group is a bit tense right now as there's some re-org going on so any hint that I'm not 100% into my team could very likely leave me in poor standing at best or unemployed at worst.
If you get caught, you want the employer to err on the side of a lighter punishment if at all possible.
To minimize the risk of getting screwed over in the worst way possible, you want to minimize the consequences to the company of doing the side business. That means any work you do would be unrelated to your current company -- make sure there isn't even the slightest inkling that what you're doing could compete with your company in any way. Do not make careless mistakes or reduce your performance in your day job -- if you end up underperforming, your company is more likely to wonder why, and more likely to be angry when they find out you've made excuses to hide the real reason.
Violating an agreement is not something looked upon kindly in most reputable businesses. Assume that any future employer will be able to learn that you have intentionally violated an employment agreement for personal profit. Think about what that will do for your future career prospects, and balance that against any additional money you would make from the side job.
Consider whether or not you will be better off if you get found out, have your employment terminated, and need to take a significant pay cut to get another job as a result.
The only way to minimize the consequences of being blackballed from future employment is to build a business that can support you 100% even if that happens. Think long and hard about whether or not you are willing to take the risk, and are getting something worth that risk in return by starting a company on the side.
Addendum (Personal Opinion)
I cannot make the decision for you, but I can't urge caution enough. The potential consequences may be worse than the benefits in the best case.
Assuming 8% interest rate, 60k loan, 20 year payback, the interest on the loan will be about 60k. Let's say you start your new business, and are able to double your loan payments (10 year payback). Your interest will drop to 27k total interest. If you lower the interest rate, or reduce the payback term, the benefit will get even lower. Let's say interest is 5%, and payback is 10 years (reduced to 5 with the side business). Now you are paying 16k in interest vs. 8k in interest -- that gap can be covered with a good raise or a promotion.
Do the math for whatever your situation is, and consider if X thousand dollars over the next Y years is really worth potentially being unemployed for the next six months.