Hey Cheddar,
Simple answer I wouldn't do it...
Here are my reasons...
1) This is being triggered by a 6 month promotional rate discount, had they not dangled a carrot would have even considered it, now I know you used the higher 3.75% rate in your math to annualize your cost vs. return, but this was incited by some cheap borrowing that was meant to get you to borrow the money you are currently not borrowing with the hope you will not pay it back within 6 months. Then the 6 months discount ends and the lender has you on the hook for the full balance at the full rate. Now they really don't care what you do with the money, as long as you pay it back, you are a good customer so they offered you a deal hoping to lend you more. Hook line and sucker. Don't be the sucker.
2) Ok forget what the lender cares about, you want to do leveraged investing, so you have $8k, not a lot of money, and like you said what if it was $16k, or $32k, more risk etc... OPM is always risky... There is a place for leveraged investing and the risk vs rewards have to be worth it, if the market makes 7% annually you will do fine over a the long term, but if it nose dives you can lose all or a lot of the principal rather quickly and not recover it for a long period of time. You still owe the debt and have to repay. Any loss is money you need to replace with other funds which diverts money from other goals, as none of this capital is yours, so the more you borrow the higher the risk. And you said you would take conservative investments so in all likelihood you would not get 7% annual returns. And of course there are taxes and inflation to account for, so how much are we really talking here?
3) You monthly payment is $96, you are overpaying by making a flat payment of $150 so you are actually reducing your HELOC balance and that compounds monthly, your new structure would divert some of that over payment to interest and your new principal balance would be higher so even though you might have investment returns in one bucket you now have a higher HELOC balance over time with less reduction in another. By the way this is contradictory to you wanting to hold onto your debt as long as possible which you have stated as this reduces it the HELOC principal. Now is your HELOC your costliest debt, if not the debt reduction should be redirected to your mortgage or SL, or eliminated completely. You can then use this extra capital to invest rather than borrow.
4) Never risk your primary residence for anything, this is a personal preference, and I know we are only talking $8k, but it is a point to make either way, you should never risk your house where you live for anything. Investment properties, equities, credit card churning etc.. that's all fair game, don't risk your house, how do you explain to your wife and kids they are homeless because you bet on black, its the same thing just not to the same extreme. Never bring your deed to Vegas or Wall Street.
5) Margin lending is a much better approach to equity leverage then Home Equity, I know you were on the thread where I mentioned IB to refi someone's student loans when they had a huge asset base and high income and someone posted it here as well. I wouldn't recommend it per se, but if you want to borrow to invest in the equity markets it is the safest way to do it, portfolio margin can be managed very effectively to prevent calls.
6) Market timing, you are looking to be aggressive in the markets and this is the 2nd situation you have posted something regarding market timing, you did a early 401k contribution as I recall. I strongly don't recommend trying to time the market, it generally will come back to bite you especially when you are not very good at knowing what you are looking for. Now I know the 401k situation has a nice long time horizon so it is a little less fair to draw an analogy but how has that worked out so far? Are you up a lot or would you have faired better making regular contributions thus far. what you are looking at here is far more risky, you want to borrow money and pay interest to invest in very volatile markets and hope you can do better, but maybe loss some or all of it, and reduce the compounding you have in debt reduction. Its a gamble at best.
You know I work on Wall Street like iostavi, and I too won't try to time the market, reason is I know I will lose. I made the mistake last year of trying my hand at a little options trading. I lost, not because I didn't know what I was doing, but because I was greedy and didn't stick to my trading plan. I broke the rules. I was doubly stupid because I funded my little venture with OPM, I used 0% credit cards figuring it was free money. Well I lost $35k of my $45k which was a blip on the radar for us financially, my portfolio bounced by that much or more this month too, however the trading mess required me to divert regular income to replace the loss as I had to pay back the credit cards, the portfolio loss will just recover naturally. It took more than a back rub to sooth it over with the wife :/
I know somewhere in a thread you were involved in there was a comment about why aren't more CPA's and financial advisors better off financially. The simple answer is they think they know better and they need to eat more humble pie... Always trying to game the system and make a little more and do a little better. Instead of sticking tot he basics that work a little knowledge is dangerous. I feel prey to that myself. I lost the $35k, now I call it a blip on the radar because I consider it risk capital and it had no tangible impact on our finances, however had I not ever gotten involved in the whole mess my guess is my net worth would probably be about $100k more now than it is due to business expenses, legal, accounting, software, the actual loss, paying it back, not being able to invest the money etc... All those mistakes add up, if I add up all my mistakes in my life they are probably worth over seven figures already...
-Mister FancyPants