Should I leverage the investments and get a second rental unit, being that this is my ultimate goal? Right now my cash holdings are about 13k including that tax-advantaged account, so I would need another 6 months to gather enough for a 10-20% downpayment.
My worry is being too heavily invested in any asset - in your case in real-estate as a landlord. Having multiple rental properties can be a great source of income, but it also exposes you to a lot of risk, especially if they are all in the same region. Your personal comfort zone may differ, but I wouldn't want more than 60% of my portfolio to be in real-estate... and I'd want 35-40% (minimum) in the market, preferably as low-cost broad-market index funds.
Real estate prices is at an alltime high here. But so are stocks (everywhere it seems).
Food for thought - the SP500 (a good measure of the US market) has reached an 'all-time high" in just over 50% of all years over the last century. Real estate prices are similar, because they (on average) match inflation. There are dips and spikes but in most years they will be higher than they ever have before.
If I choose to leverage my total debt will be more than doubled. If interest rates then rise to 6-8% over the next few years it might hurt my finances badly unless rental prices also picks up. Is it therefore wise to fix the interest rates on the mortages?
This is perhaps the best reason to also have money invested in equities and bonds. Right now mortgages in the US are near historical lows, and near historical inflation rates. If your mortgages aren't fixed, now is a very good time to look into having them fixed.
Also, rental rates typically move with interest rates (they are strongly correlated). that's because landlords raise the rent whenever their mortgages go up, and it becomes less 'affordable' for people to buy their own home.
When debating this with a smart friend of mine, he asked me the following: "Imagine you had no debt and no savings right now. Would you take on debt and invest the money?" My answer was no and he told me that's a good reason to pay down my debts before investing.
I'm not sure I agree with your friend's line of thinking, and given your talk of 'leveraging' to increase real-estate holdings, i'm not sure you do either.
From where I sit, you should ignore these alternative reality scenarios and only focus on what you have now and what your best course of action could be. With interest rates below 3%, from a purely financial standpoint it makes the most sense to pay the minimum and invest the difference. Inflation (at 2-2.5%) will nullify virtually all the interest you pay each year, and the likelihood that you will earn >3% before inflation has historically been a lock over longer time periods.
Also, if someone offered me the chance today of taking out a $98k loan @ 2.8% without needing to go to school or purchase another house... hell yes I'd do it. I could cover the monthly payments and I would put it all into my index fund.