HI @Andrew Dincola! You are a ways ahead of being a newbie I would say. Though you may be a newbie in property count, you definitely have a defined vision and goal that you want to achieve! This is the #1 thing I suggest anyone tackle before getting into investing. Now it is just figuring out how to best achieve this goal of $3k a month for you.
I agree with what David said above me, but I believe you can get to the goal that you have in mind sooner, and easier than you believe. If FI is your goal, and you want to achieve this ASAP, I would suggest you continue house hacking here in Denver each and every year. If you are not worried about loosing some comfort, I would suggest sticking to rent by the room, and really supercharge your FI.
If you qualify for a traditional mortgage, and you are able to acquire a 5-6 bedroom home here in the Denver area for between 450-500k (with the current prices of homes) then by renting out the other 4-5 rooms that you and the GF don't occupy, you will be able to live for free, and producing cashflow. An average room in Denver goes for about $700 a month (some for more) so if you rent 4-5 you'll be looking at around 2800-3500 a month in rental income (while you live there, adding 700 when you move out). It is not unheard of for my clients to be making $1000 on top of their mortgage while they occupy the home, and are living for free. So with that you would just need to buy one of these properties every year for the next 3 years and you'll hit your goal.
But remember, you are also living for free, and can accelerate your savings rate. So the way I suggest people strategize is after they get into their first house hack, begin saving for the next DP (about 25k for an average home here), then when you have that saved the rest of the year you can put the extra savings towards other investments like out of state. If you can purchase 1 house hack, and 1 out of state investment each year that would get you to your goal in no time (relatively speaking).
I would agree that you should keep your current place, if its able to cashflow as a rental, and you may be able to pull out the equity in other ways. But if you need to sell off that property in order to get into a more optimized property (whether because you can't qualify or whatever the reason), then I would say go for it. I would also say that while the small multifamily is the traditional way to go for a house hack, it is not the best way here in Denver. Our small multifamily properties tend to be old, torn, and over priced, there are other ways to achieve the multifamily feel of a house hack, without paying that high price tag. Say renting out a finished basement unit in a single-family.
Finally, as I realize I've been ranting for a while now. While the BRRRR strategy is great, and everyone wants to utilize it, it does come with the some drawbacks. The biggest one you already pointed out... If you are BRRRing then you sacrifice cashflow in order to pull your money back out, so you need more properties in order to achieve the same amount of cashflow. The other issue is that BRRRR is usually more suited for lower price areas, like the mid west, as adding 20% in value is much easier on a 50k property, than it is on a 500k property. So unless you get really good at finding off market properties here in Denver, a full BRRRR is probably going to be tough. But if you change your mindset, and are up for sacrificing some short term comfort for long term gain you can very quickly achieve your goal without having to acquire 20 properties.
There are also multitudes of other house hack strategies that work well here, and I'm more than happy to help you find the best pass to your goal!