@Scott Bidwell I'm glad to see this thread got better with time and people actually started giving options instead of telling you it can't be done.
The reality is 1.5 million liquid is a lot of money even now. This isn't that difficult and if you were extremely motivated all of what you wanted could be done in 1 year or less (not even 3 years). I'm not saying you should approach it that way but it is very possible to buy 10 rentals and your own 450k home when you have that kind of cash regardless of having another real income.
Buying 10 rentals with 500k is not that difficult (for experienced investors) using the right lenders which there are several. Buying one decent deal a month isn't that difficult and getting it fixed then rented to pull the even 1/3 of your down payment back out will get you to 7 or 8 houses. Once you get the system down the last 5 months you could buy more than one and you would have more than 10 even if your lender needed a renter in there for 4 months in order to refi. You have 1.5M and you said in 3 years so this becomes a walk in the park. If people are saying it is difficult or giving you lectures then I question whether they are really investing or they are just saving. Nothing wrong with saving but it is a very slow way to get to independent money.
I'm not even considering owner finance solutions to get you to these numbers which others rightfully stated above can help.
Structuring things to get to your goals is not the hard part because of your low capital restraints. Great deals that get you back most of your money on each deal is the hardest thing. But you don't need to get most of the money back on each deal since you will be able to use 10 to 20 percent hard money bridge loans then get some of that back. Your money will go a very long way.
As for getting you the home you wanted you really could pay cash and have enough left over to reach the goals you put out. But I can think of plenty of ways you can show income without actually having to do any kind of difficult work.
If your existing lender can use investment income for your loan then loaning money per project to a flipper should be able to get you plenty of income to show. As an example we have gap fund investors that make can make 5k to 20k on a 50k loan in 2 months worse case they make a min of interest and points but we add equity so when a deal does well the numbers go up dramatically. If you ran that scenario with 1 million (keeping 500k for your brrrs) and we used 5k per deal profit. Then your income is 50k per month (not realistic that would assume every dollar was always active and turned exactly every 2 months but its a start). So let's cut that down to saying half the money was actively invested and each deal averaged 3 months time and still only the 5k per deal which is low. This puts your income at 16,666 per month. This is the low-end IMO for this kind of deal structure. That is more than enough for the 450k loan to go through and leave you 500k for brrrr investments, and the flips you are funding (with risk of course) are making you 200k per year in income through equity and interest (talk to a tax expert of course).
If you need actual income from a job to get the loan its possibly too. I'm sure if you are loaning that kind of money someone would give you a "job" that paid you something and then lowered your investment return on the money. Probably want to be careful with how this goes down but I'm just trying to give you ideas that might spark or lead to more ideas.
I'll stop rambling now but I think you should go for it. Start out with a deal or two to get your feet wet. Probably need to stay in some markets under 400k preferably 300k or less really but its totally doable. Look up the lender types mentioned above, bridge lenders etc. They will help you recapture some of you capital making it go further.